BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andreas Petersson (University of Oslo) DTSTART:20200918T090000Z DTEND:20200918T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/1 DESCRIPTION:Title: Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs\nby Andreas Peterss on (University of Oslo) as part of STAR seminars\n\n\nAbstract\nWe conside r the computation of quadratic functionals of the solution to a linear par abolic stochastic partial differential equation (SPDE) with multiplicative Gaussian noise on a bounded domain. The functionals are allowed to be pat h dependent and the noise is white in time and may be white in space. An o perator valued Lyapunov equation\, whose solution admits a deterministic r epresentation of the functional of the SPDE solution\, is used for this pu rpose and error estimates are shown in suitable operator norms for a fully discrete approximation of this equation. We also use these estimates to d erive weak error rates for a fully discrete approximation of the SPDE itse lf. In the setting of finite element approximations\, a computational comp lexity comparison reveals that approximating the Lyapunov equation allows us to compute quadratic functionals more cheaply compared to applying Mont e Carlo or covariance-based methods directly to the discretized SPDE. We i llustrate the theoretical results with numerical simulations.\nThis is joi nt work with Adam Andersson\, Annika Lang and Leander Schroer.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Emel Savku (University of Oslo) DTSTART:20200925T090000Z DTEND:20200925T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/2 DESCRIPTION:Title: Optimal investment strategies in a Markov Regime-Switc hing Market\nby Emel Savku (University of Oslo) as part of STAR semina rs\n\n\nAbstract\nWe discuss two optimal investment problems by using zero -sum and nonzerosum stochastic game approaches in a continuous-time Markov regimeswitching jump-diffusion environment. We represent different states of an economy by a D-state Markov chain. The first application is a zero- sum game between an investor and the market\, and the second one formulate s a nonzerosum stochastic differential portfolio game as the sensitivity o f two investors’ terminal gains.We derive regime-switching Hamilton–Ja cobi–Bellman–Isaacs equations and obtain explicit optimal portfolio st rategies.We illustrate our results in a two-state special case and observe the impact of regime switches by comparative results.\nJoint work with Ge rhard Wilhem Weber.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasmina Djordjevic (University of Oslo) DTSTART:20201002T090000Z DTEND:20201002T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/3 DESCRIPTION:Title: Perturbation effect on Reflected Backward Stochastic D ifferential Equations\nby Jasmina Djordjevic (University of Oslo) as p art of STAR seminars\n\n\nAbstract\nPerturbed stochastic differential equa tions\, in general\, are the topic of permanent interest of many authors\, both theoretically and in applications. Stochastic models of complex phen omena under perturbations in analytical mechanics\, control theory and pop ulation dynamics\, for example\, can be sometimes compared and approximate d by appropriate unperturbed models of a simpler structure. In this way\, the problems can be translated into more simple and familiar cases which a re easier to solve and investigate. Problems of perturbed backward stochas tic differential equations (BSDEs) are very interesting because of their a pplications in economy and finance. The most interesting problem in this f ield of perturbations of BSDEs deals with a large class of reflected backw ard stochastic differential equations whose generator\, barrier process an d final condition are arbitrarily dependent on a small parameter. The solu tion of perturbed equation\, is compared in the L p -sense\, with the solu tions of the appropriate unperturbed equations. Conditions under which the solution of the unperturbed equation is L p -stable are given. It is show n that for an arbitrary η > 0 there exists an interval [t(η)\, T] ⊂ [0 \, T] on which the L p -difference between the solutions of both the pertu rbed and unperturbed equations is less than η.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Rydin Gorjão (Institute of Theoretical Physics\, Univers ity of Cologne) DTSTART:20201009T090000Z DTEND:20201009T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/4 DESCRIPTION:Title: Applications and developments of stochastic processes in power-grid frequency measurements: A data-driven study.\nby Leonard o Rydin Gorjão (Institute of Theoretical Physics\, University of Cologne) as part of STAR seminars\n\n\nAbstract\nPower-grid frequency is a key mea surement of stability of power-grid systems. It comprises the balance of p ower generation and consumption\, electricity market exchanges\, and contr ol mechanism. Power-grid frequency\, as stochastic process\, has been scar cely studied. We will present the developments in power-grid frequency dat a collection\, the design of a N-dimensional non-parametric estimator for time-continuous Markov processed\, and the design of a computationally eff icient Multifractal Detrended Fluctuation Analysis (MFDFA) algorithm. Last ly\, we will report on the design of a surrogate stochastic model for powe r-grid frequency via a fractional Ornstein–Uhlenbeck process\, the appli cation of a Hurst index and a volatility estimator\, and the limitations d ue to multifractional and time-and-space coloured noise.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Sanz-Solé (University of Barcelona) DTSTART:20201016T090000Z DTEND:20201016T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/5 DESCRIPTION:Title: Stochastic wave equations with super-linear coefficien ts\nby Marta Sanz-Solé (University of Barcelona) as part of STAR semi nars\n\n\nAbstract\nWe consider a stochastic wave equation on R^d \, d ∈ {1\, 2\, 3}\, driven by a Gaussian noise in (t\, x)\, white in time. We a ssume that the free terms b and σ are such that\, for |x| → ∞\, \n|σ (x)| ≤ σ_1 + σ2_|x| (ln_+(|x|))^a \, |b(x)| ≤ θ_1 + θ_2|x| (ln_+(| x|))^δ \, (1) \nwhere θ_2\, σ_2 > 0\, δ\, a > 0\, with b dominating ov er σ. For any fixed time horizon T > 0 and with a suitable constraints on the parameters a\, δ\, σ_2 and θ_2\, we prove existence of a random fi eld solution to the equation and that this solution is unique\, and bounde d in time and in space a.s. The research is motivated by the article [R. D alang\, D. Khoshnevisan\, T. Zhang\, AoP\, 2019] on a 1-d reaction-diffusi on equation with coefficients satisfying conditions similar to (1). We see that the L^∞- method used by these authors can be successfully implemen ted in the case of wave equations. This is joint work with A. Millet (U. P aris 1\, Panthéon-Sorbonne)​.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Samy Tindel (Purdue University) DTSTART:20201023T090000Z DTEND:20201023T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/6 DESCRIPTION:Title: A coupling between Sinai’s random walk and Brox diff usion\nby Samy Tindel (Purdue University) as part of STAR seminars\n\n \nAbstract\nSinai’s random walk is a standard model of 1-dimensional ran dom walk in random environment. Brox diffusion is its continuous counterpa rt\, that is a Brownian diffusion in a Brownian environment. The convergen ce in law of a properly rescaled version of Sinai’s walk to Brox diffusi on has been established 20 years ago. In this talk\, I will explain a stra tegy which yields the convergence of Sinai’s walk to Brox diffusion than ks to an explicit coupling. This method\, based on rough paths techniques\ , opens the way to rates of convergence in this demanding context. Notice that I’ll try to give a maximum of background about the objects I’m ma nipulating\, and will keep technical considerations to a minimum.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaozhong Hu (University of Alberta) DTSTART:20201106T100000Z DTEND:20201106T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/7 DESCRIPTION:Title: Functional central limit theorems for stick-breaking p riors\nby Yaozhong Hu (University of Alberta) as part of STAR seminars \n\n\nAbstract\nWe obtain the empirical strong law of large numbers\, empi rical \nGlivenko-Cantelli theorem\, central limit theorems\, \nfunctional central limit theorems for various nonparametric Bayesian priors\nwhich i nclude the Dirichlet process with general stick-breaking weights\, \n the Poisson-Dirichlet process\, the normalized inverse Gaussian \nproce ss\, the normalized generalized gamma \nprocess\, and the generaliz ed Dirichlet process. \nFor the Dirichlet process with general stick-brea king weights\, \nwe introduce two general conditions such that the central limit theorem holds. \nExcept in the case of generalized Dirichlet proces s\, since the finite dimensional \ndistributions of these processes are e ither hard to obtain or are \ncomplicated to use even they are available\, \nwe use the general moment method to obtain the convergence results. \nFor the generalized Dirichlet process we use its finite dimensional mar ginal distributions to obtain the asymptotics although \nthe computation s are highly technical.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rama Cont (University of Oxford) DTSTART:20201113T100000Z DTEND:20201113T111500Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/8 DESCRIPTION:Title: Excursion risk\nby Rama Cont (University of Oxford ) as part of STAR seminars\n\n\nAbstract\nA broad class of dynamic trading strategies may be characterized in terms of excursions of the market pr ice of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies\, based on a descript ion in terms of price excursions\, first in a pathwise setting\, without p robabilistic assumptions\, then in a probabilistic setting\, when the pric e is modelled as a Markov process.\n\nWe introduce the notion of δ-excurs ion\, defined as a path which deviates by δ from a reference level befor e returning to this level. We show that every continuous path has a unique decomposition into such δ-excursions\, which turn out to be useful for t he scenario analysis of dynamic trading strategies\, leading to simple exp ressions for the number of trades\, realized profit\, maximum loss and dra wdown. \nWhen the underlying asset follows a Markov process\, we combine t hese results with Ito's excursion theory to obtain a tractable decompositi on of the process as a concatenation of independent δ-excursions\, whose distribution is described in terms of Ito's excursion measure. We provide analytical results for linear diffusions and give new examples of stochas tic processes for flexible and tractable modeling of excursions. Finally\, we describe a non-parametric scenario simulation method for generating pa ths whose excursions match those observed in a data set.\n\nThis is joint work with: Anna Ananova and RenYuan Xu.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Federica Masiero (University of Milano-Bicocca) DTSTART:20201218T100000Z DTEND:20201218T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/9 DESCRIPTION:Title: Regularizing properties and HJB equations for stochast ic problems with delay\nby Federica Masiero (University of Milano-Bico cca) as part of STAR seminars\n\n\nAbstract\nIn this talk we consider stoc hastic differential equations with delay.\nIt is well known that the Ornst ein-Uhlenbeck transition semigroup doesn’t have regularizing properties\ , such as the strong Feller property. So in general\, the associated Hamil ton-Jacobi-Bellman (HJB) equation cannot be solved in mild sense by a clas sical fixed point argument. We present a result of existence of regular so lutions for the HJB equations related to a stochastic controlled equation with delay in the control and in the case when\, as it often occurs in app lications\, the objective function depends only on the “present” of th e state and control variable. The result is based on partial regularizatio n results for the associated Ornstein-Uhlenbeck semigroup.\nIn analogy\, w e investigate partial reularizing properties in the case of delay in the s tate and with a special dependence on the past trajectory\, and we solve i n mild sense the associated HJB equation and the stochastic controlled pro blem related.\n\nThe talk is mainly based on joint works with F. Gozzi and G. Tessitore.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tusheng Zhang (University of Manchester) DTSTART:20201120T100000Z DTEND:20201120T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/10 DESCRIPTION:Title: Reflected Brownian motion with measure-valued drifts< /a>\nby Tusheng Zhang (University of Manchester) as part of STAR seminars\ n\n\nAbstract\nIn this talk\, I will present some recent results on the un iqueness and existence of weak solution to the reflected Brownian motion with measure-valued drifts. Furthermore\, we obtain some Gaussian type est imates of the transition density function of the solution and we also p rovide solutions to the associated Neumann boundary value problems.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ruiz Banos (University of Oslo) DTSTART:20201204T100000Z DTEND:20201204T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/11 DESCRIPTION:Title: Life and pension insurance policies with random cash flows subject to interest rate regimes\nby David Ruiz Banos (Universit y of Oslo) as part of STAR seminars\n\n\nAbstract\nA life or pension insur ance is a contract between an insurance company and a person\, where the i nsurer promises to pay a sum of money\, either at once or periodically\, t o the insured or a beneficiary (e.g. family member) under some specified e vents. Actuaries must assess the value of such contracts and their risk. F or example\, how much is it worth today a pension agreement for a 30 year old Norwegian citizen consisting of a yearly pension of NOK200 000 from a retirement age of 70 years? This question\, although it may seem easy to a nswer\, is not. There are two main risks for such contract from the insura nce company perspective. First\, interest rate risk (too low/high interest ) and logenvity or mortality risk (wrong forecast of mortality).\n\nIn thi s talk we will discuss interest rate risk and derive a formula for the val ue of insurance contracts where the cash flow (e.g. NOK200 000) is also ra ndom\, and not fixed. For example: a pension which pays NOK200 000 in high interest rate regimes and NOK150 000 in low interest rate regimes.\nWe wi ll introduce the main and basic definitions and concepts for those who are not acquainted with it. Then we will derive the so-called Thiele's partia l differential equation for computing prospective reserves and finally we will look at specific examples under the Vasicek model by either solving t he problem explicitly (tedious but worth it) or numerically (implicit and explicit finite difference method).\nFinally\, we will also overview some possible open questions and future research plans.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Arne Bang Huseby (University of Oslo) DTSTART:20210115T100000Z DTEND:20210115T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/12 DESCRIPTION:Title: Optimal reinsurance contracts in the multivariate cas e\nby Arne Bang Huseby (University of Oslo) as part of STAR seminars\n \n\nAbstract\nAn insurance contract implies that risk is ceded from ordina ry policy holders to companies. However\, companies do the same thing bet ween themselves. This is known as reinsurance\, and the ceding company is known as the cedent. The rationale could be the same\; i.e.\, that a fin ancially weaker agent is passing risk to a stronger one. In reality even t he largest companies do this to diversify risk\, and financially the ceden t may be as strong as the reinsurer. The problem of determining re­in­s u­rance contracts which are optimal with respect to some reasonable crite rion has been studied extensively within actuarial science. Different con tact types are considered such as stop-loss contracts where the reinsuranc e company covers risk above a certain level\, and insurance layer contract s where the reinsurance company covers risk within an interval. The contr acts are then optimized with respect to some risk measure\, such as value- at risk (VaR) or conditional tail expectation (CTE).\nIn this seminar we c onsider the problem of minimizing VaR in the case of multiple insurance la yer contracts. Such contracts are known to be optimal in the univariate c ase\, and the optimal contract is easily determined. In the multivariate case\, however\, finding the optimal set of contracts is not easy. In fac t the optimal contract is not even unique in this case. Still by consider ing solutions where the risk is balanced between the contracts\, a solutio n can be found using an iterative Monte Carlo method.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Josep Vives (University of Barcelona) DTSTART:20210129T100000Z DTEND:20210129T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/13 DESCRIPTION:Title: Decomposition and high order approximation of option prices. Some applications to Heston\, Bates\, CEV and rough volatility mod els\nby Josep Vives (University of Barcelona) as part of STAR seminars \n\n\nAbstract\nUsing Itô calculus techniques we present an option price decomposition for local and stochastic volatility jump diffusion models an d we use it to obtain fast and accurate approximations of call option pric es for different local or stochastic volatility models.\n\nThe main purpos e is to present the ideas given in the recent paper:\n\nA. Gulisashvili\, M. Lagunas\, R. Merino and J. Vives (2020): “Higher order approximation of call option prices in stochastic volatility models”. Journal of Compu tational Finance 24 (1).\n\nBut I will also comment ideas of the papers:\n \nE. Alòs\, R. De Santiago and J. Vives (2015): “Calibration of stochas tic volatility models via second order approximation: the Heston case”. International Journal of Theoretical and Applied Finance 18 (6): 1550036 ( 31 pages).\n\nJ. Vives (2016): “Decomposition of the pricing formula for stochastic volatility models based on Malliavin – Skorohod type calculu s”. Proocedings of the Research School CIMPA-UNESCO-MSER-MINECO-MOROCCO on Statistical Methods and Applications in Actuarial Science and Finance 2 013. Springer.\n\nR. Merino and J. Vives (2017): “Option price decomposi tion in local volatility models and some Applications”. International Jo urnal of Stochastic Analysis. Volume 2017\, Article ID 8019498\, 16 pages\ n\nR. Merino\, J. Pospísil\, T. Sobotka and J. Vives (2018): “Decomposi tion formula for jump diffusion models”. International Journal of Theore tical and Applied Finance 21 (8).\n\nR. Merino\, J. Pospisil\, T. Sobotka\ , T. Sottinen and J. Vives (2021): “Decomposition formula for rough Volt erra stochastic volatility models”. Submitted.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Emil R. Framnes (Global Head of Trading Norges Bank Investment Man agement) DTSTART:20210212T100000Z DTEND:20210212T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/14 DESCRIPTION:Title: Equity trading at NBIM\nby Emil R. Framnes (Globa l Head of Trading Norges Bank Investment Management) as part of STAR semin ars\n\n\nAbstract\nEmil will give an introduction to Norges Bank Investmen t Management and its trading operations. His presentation will mainly focu s on trading in equity markets and feature some of the dynamics and charac teristics of the equity market and explain how various participants like i nstitutional managers\, high frequency traders and retail clients trade an d shape equity markets today.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nacira Agram (Linnaeus University) DTSTART:20210219T100000Z DTEND:20210219T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/15 DESCRIPTION:Title: Deep learning and stochastic mean-field control for a neural network model\nby Nacira Agram (Linnaeus University) as part o f STAR seminars\n\n\nAbstract\nWe study a membrane voltage potential model by means of stochastic control of mean-field stochastic differential equ ations and by machine learning techniques. The mean-field stochastic contr ol problem is a new type\, involving the expected value of a combination o f the state X(t) and the running control u(t) at time t. Moreover\, the co ntrol is two-dimensional\, involving both the initial value z of the state and the running control u(t).\nWe prove a necessary condition for optimal ity and a verification theorem of a control (u\; z) for such a general sto chastic mean-field problem. The results are then applied to study a partic ular case of a neural network problem\, where the system has a drift given by E[u(t)X(t)] and the problem is to arrive at a terminal state value X(T ) which is close in terms of variance to a given terminal value F under mi nimal costs\, measured by z^2 and the integral of u^2(t).\nThis problem is too complicated to handle by mathematical methods alone. We solve it usin g deep learning techniques.\nThe talk is based on joint work with A. Bakdi and B. Øksendal at University of Oslo.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Annika Lang (Chalmers University of Technology) DTSTART:20210305T100000Z DTEND:20210305T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/16 DESCRIPTION:Title: The stochastic wave equation on the sphere: propertie s and simulation\nby Annika Lang (Chalmers University of Technology) a s part of STAR seminars\n\n\nAbstract\nThe stochastic wave equation driven by isotropic Gaussian noise is considered on the unit sphere. We solve th is stochastic partial differential equation and discuss properties of the derived solutions. These are used in the developed approximation scheme ba sed on spectral methods and its convergence analysis. We derive strong\, w eak\, and almost sure convergence rates for the proposed algorithm and sho w that these rates depend only on the smoothness of the driving noise\, th e initial conditions\, and the test functions. Numerical experiments confi rm the theoretical rates. Finally we discuss extensions to more general do mains and equations that can be treated in a similar way.\nThis talk is ba sed on joint work with David Cohen\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Lobbe (University of Oslo) DTSTART:20210319T100000Z DTEND:20210319T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/17 DESCRIPTION:Title: Pathwise approximations for the solution of the non-l inear filtering problem\nby Alexander Lobbe (University of Oslo) as pa rt of STAR seminars\n\n\nAbstract\nStochastic Filtering deals with the rec overy of the state of a signal process from noisy observations.\nFiltering models are ubiquitous within science and engineering\, weather prediction being only one important example. In such applications\, accurate\, fast\ , and stable algorithms for the approximation of the filtering functional are essential.\nAfter introducing the stochastic filtering framework\, we consider high order approximations of the solution of the stochastic filte ring problem and derive their pathwise representation in the spirit of ear lier work by Clark and Davis. The robustness property of the derived appro ximation is subsequently proved. Thus\, we establish that the high order d iscretised filtering functionals can be represented by Lipschitz continuou s functions defined on the observation path space.\nJoint work with Dan Cr isan and Salvador Ortiz-Latorre\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Lyudmila Grigoryeva (University of Kostanz) DTSTART:20210430T090000Z DTEND:20210430T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/18 DESCRIPTION:Title: Discrete-time signatures and randomness in reservoir computing\nby Lyudmila Grigoryeva (University of Kostanz) as part of S TAR seminars\n\n\nAbstract\nA new explanation of geometric nature of the r eservoir computing phenomenon is presented. Reservoir computing is underst ood in the literature as the possibility of approximating input/output sys tems with randomly chosen recurrent neural systems and a trained linear re adout layer. Light is shed on this phenomenon by constructing what is call ed strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions. This proc edure yields a state-affine reservoir system with randomly generated coeff icients in a dimension that is logarithmically reduced with respect to the original system. This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear re adout for each different filter. Explicit expressions for the probability distributions needed in the generation of the projected reservoir system a re stated and bounds for the committed approximation error are provided.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Arne Løkka (London School of Economics) DTSTART:20210416T090000Z DTEND:20210416T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/19 DESCRIPTION:Title: Foreign exchange equilibrium\, international trade an d trading costs\nby Arne Løkka (London School of Economics) as part o f STAR seminars\n\n\nAbstract\nIn this paper we prove existence and unique ness of an equilibrium for an international economy consisting of two sepa rate economies and a complete financial market. Each economy produce a sin gle perishable good and trade between the two economies carries proportion al trading costs. In each economy there are a number of agents aiming to m aximise their expected utility of consumption of the single perishable goo d. We draw on the methods used for the one economy case using the Negishi argument\, and obtain semi-explicit formulas for the equilibrium solutions . In order to prove uniqueness\, we establish that for any equilibrium\, t he consumptions must be Pareto optimal. To account for the costs of tradin g between the economies\, this requires a modification of the standard not ion of feasible allocations and Pareto optimality.\n\nOur results therefor e generalise the theory for the one economy in a number of interesting way s that offer new insights and perspectives. \nModels of international econ omies with proportional trading costs have received a lot of attention in economics\, but as far as we know\, existence and uniqueness of an equilib rium have not rigorously been established.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Crisan (Imperial College London) DTSTART:20210507T090000Z DTEND:20210507T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/20 DESCRIPTION:Title: Well-posedness Properties for a Stochastic Rotating S hallow Water Model\nby Dan Crisan (Imperial College London) as part of STAR seminars\n\n\nAbstract\nThe rotating shallow water (RSW) equations d escribe the evolution of a compressible rotating fluid below a free surfac e. The typical vertical length scale is assumed to be much smaller than th e horizontal one\, hence the shallow aspect. The RSW equations are a simpl ification of the primitive equations which are the equations of choice for modelling atmospheric and oceanic dynamics. In this talk\, I will present some well-posedness properties of a viscous rotating shallow water syste m. The system is stochastically perturbed in such a way that two key prope rties of its deterministic counterpart are preserved. First\, it retains t he characterisation of its dynamics as the critical path of a variational problem. In this case\, the corresponding action function is stochasticall y perturbed. Secondly\, it satisfies the classical Kelvin circulation theo rem. The introduction of stochasticity replaces the effects of the unreso lved scales. The stochastic RSW equations are shown to admit a unique max imal strong solution in a suitably chosen Sobolev space which depends cont inuously on the initial datum. The maximal stopping time up to which the s olution exist is shown to be strictly positive and\, for sufficiently sma ll initial datum\, the solution is shown global in time with positive prob ability. This is joint work with Dr Oana Lang (Imperial College London) an d forms part of the ERC Synergy project “Stochastic transport in upper o cean dynamics”\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Lord (Radboud University) DTSTART:20210521T090000Z DTEND:20210521T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/21 DESCRIPTION:Title: Adaptive time-stepping for S(P)DEs​\nby Gabriel Lord (Radboud University) as part of STAR seminars\n\n\nAbstract\nWe pres ent how adaptive time-stepping might be used to solve SDEs with non-Lipsch itz drift (and potentially diffusion) combined with a tamed or similar met hod. We illustrate how to pick the timestep and look at strong convergence . We then consider the extension to stochastic PDEs and will mention the two cases of additive and multiplicative noise and illustrate the results numerically.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrey Dorogovtsev (National Academy of Science of Ukraine) DTSTART:20210611T090000Z DTEND:20210611T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/22 DESCRIPTION:Title: Occupation and evolutionary measure-valued processes< /a>\nby Andrey Dorogovtsev (National Academy of Science of Ukraine) as par t of STAR seminars\n\n\nAbstract\nn the talk we consider two types of meas ure-valued processes constructed from the processes on the phase space. Th ese are visitation processes and solutions to equations with interactions. We will discuss questions of stability and stochastic calculus for such p rocesses. Applications to construction of loop eraised random walks are pr esented.\nThe talk is based on the joint work with Iryna Nishchenko and Ja smina Đorđević.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Ralf Korn (University of Kaiserslautern) DTSTART:20210820T090000Z DTEND:20210820T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/23 DESCRIPTION:Title: Least-Squares MC for Proxy Modeling in Life Insurance : Linear Regression and Neural Networks\nby Ralf Korn (University of K aiserslautern) as part of STAR seminars\n\n\nAbstract\nThe Solvency Capita l Requirement (SCR) is the amount of Available Capital that an insurer has to provide to be solvent by the end of the year with a probability of (at least) 99.5%. Due to regulations\, the SCR should be calculated from the distribution of the one-year loss if the insurer uses an interal model. G iven the complicated cash flow projections of a life insurer\, this calcul ation is a tremendous task and cannot be performed by a crude Monte Carlo approach. In this talk\, we show how to overcome computational complexity by using the so called least-squares Monte Carlo approach in combination w ith both linear regression and a feedforward neural network. Here\, it is particularly challenging to obtain the so-called ground truth to calibrate our models.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano De Marco (Ecole Polytechnique Palaiseau) DTSTART:20210917T090000Z DTEND:20210917T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/24 DESCRIPTION:Title: On the implied and local volatility surfaces generate d by rough volatility\nby Stefano De Marco (Ecole Polytechnique Palais eau) as part of STAR seminars\n\n\nAbstract\nSeveral asymptotic results fo r the implied volatility generated by a rough volatility model have been o btained in recent years (notably in the small-maturity regime)\, providing a better understanding of the shapes of the volatility surface induced by such models\, and supporting their calibration power to SP500 option data .\nRough volatility models also generate a local volatility surface\, via the Markovian projection of the stochastic volatility (equivalently\, via Dupire's formula applied to the model's option price surface). We compleme nt the existing results with the asymptotic behavior of the local volatili ty surface generated by a class of rough stochastic volatility models enco mpassing the rough Bergomi model.\nNotably\, we observe that the celebrate d "1/2 skew rule" linking the short-term at-the-money (ATM) skew of the im plied volatility to the short-term ATM skew of the local volatility\, a co nsequence of the celebrated "harmonic mean formula" of [Berestycki\, Busca \, and Florent\, QF 2002]\, is replaced by a new rule: the ratio of the im plied volatility and local volatility ATM skews tends to the constant 1/(H + 3/2) (as opposed to the constant 1/2)\, where H is the regularity index of the underlying instantaneous volatility process.\nJoint work with Flo rian Bourgey\, Peter Friz\, and Paolo Pigato.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Rosenbaum (Ecole Polytechnique Palaiseau) DTSTART:20211001T090000Z DTEND:20211001T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/25 DESCRIPTION:Title: A rough volatility tour from market microstructure to VIX options via Heston and Zumbach.\nby Mathieu Rosenbaum (Ecole Poly technique Palaiseau) as part of STAR seminars\n\n\nAbstract\nIn this talk\ , we present an overview of recent results related to the rough volatility paradigm. We consider both statistical and option pricing issues in this framework. We notably connect the behaviour of high frequency prices to th at of implied volatility surfaces\, even for complex products such as the VIX.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Blanka Hovarth (King's College London) DTSTART:20210903T090000Z DTEND:20210903T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/26 DESCRIPTION:Title: Data-Driven Market Simulators some simple applicatons of signature kernel methods in mathematical finance\nby Blanka Hovart h (King's College London) as part of STAR seminars\n\n\nAbstract\nTechniqu es that address sequential data have been a central theme in machine learn ing research in the past years. More recently\, such considerations have e ntered the field of finance-related ML applications in several areas where we face inherently path dependent problems: from (deep) pricing and hedgi ng (of path-dependent options) to generative modelling of synthetic market data\, which we refer to as market generation.\nWe revisit Deep Hedging f rom the perspective of the role of the data streams used for training and highlight how this perspective motivates the use of highly accurate genera tive models for synthetic data generation. From this\, we draw conclusions regarding the implications for risk management and model governance of th ese applications\, in contrast torisk-management in classical quantitative finance approaches.\nIndeed\, financial ML applications and their risk-ma nagement heavily rely on a solid means of measuring and efficiently comput ing (smilarity-)metrics between datasets consisting of sample paths of sto chastic processes. Stochastic processes are at their core random variables with values on path space. However\, while the distance between two (fini te dimensional) distributions was historically well understood\, the exten sion of this notion to the level of stochastic processes remained a challe nge until recently. We discuss the effect of different choices of such met rics while revisiting some topics that are central to ML-augmented quantit ative finance applications (such as the synthetic generation and the evalu ation of similarity of data streams) from a regulatory (and model governan ce) perpective. Finally\, we discuss the effect of considering refined met rics which respect and preserve the information structure (the filtration) of the marketand the implications and relevance of such metrics on financ ial results.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Galinberti (NTNU Trondheim) DTSTART:20211015T090000Z DTEND:20211015T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/27 DESCRIPTION:Title: Neural Networks in Fréchet spaces\nby Luca Galin berti (NTNU Trondheim) as part of STAR seminars\n\n\nAbstract\nIn this tal k we present some novel results obtained by Fred Espen Benth (UiO)\, Nils Detering (University of California Santa Barbara) and myself on abstract n eural networks and deep learning. More precisely\, we derive an approximat ion result for continuous functions from a Fréchet space $X$ into its fie ld $\\mathbb{F}\, (\\mathbb{F}\\in\\{\\mathbb{R}\,\\mathbb{C} \\})$. The a pproximation is similar to the well known universal approximation theorems for continuous functions from $\\mathbb{R}^n$ to $\\mathbb{R}$ with (mult ilayer) neural networks by Cybenko\, Hornik et al.\, Funahashi\, Leshno et al. Similar to classical neural networks\, the approximating function is easy to implement and allows for fast computation and fitting. Few applica tions geared toward derivative pricing and numerical solutions of paraboli c partial differential equations will be outlined.\n\nReferences:\n\nG. Cy benko. Approximation by superpositions of a sigmoidal function. Mathematic s of Control\, Signals and Systems\, 2(4):303–314\, 1989.\n\nK. Hornik\, M. Stinchcombe\, and H. White. Multilayer feedforward networks are univer sal approximators. Neural Networks\, 2(5):359–366\, 1989. \n\nK.-I. Funa hashi. On the approximate realization of continuous mappings by neural net works. NeuralNetworks\, 2(3):183–192\, 1989. \n\nM. Leshno\, V. Y. Lin\, A. Pinkus\, and S. Schocken. Multilayer feedforward networks with a nonpo lynomial activation function can approximate any function. Neural Networks \, 6(6):861–867\, 1993.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Asma Khedher (University of Amsterdam) DTSTART:20211105T090000Z DTEND:20211105T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/28 DESCRIPTION:Title: An infinite-dimensional affine stochastic volatility model\nby Asma Khedher (University of Amsterdam) as part of STAR semin ars\n\n\nAbstract\nWe introduce a flexible and tractable infinite-dimensio nal stochastic volatility model. More specifically\, we consider a Hilbert space valued Ornstein–Uhlenbeck-type process\, whose instantaneous cova riance is given by a pure-jump stochastic process taking values in the con e of positive self-adjoint Hilbert-Schmidt operators. The tractability of our model lies in the fact that the two processes involved are jointly aff ine\, i.e.\, we show that their characteristic function can be given expli citly in terms of the solutions to a set of generalised Riccati equations. The flexibility lies in the fact that we allow multiple modeling options for the instantaneous covariance process\, including state-dependent jump intensity.\nInfinite dimensional volatility models arise e.g. when conside ring the dynamics of forward rate functions in the Heath-Jarrow-Morton-Mus iela modeling framework using the Filipović space. In this setting we dis cuss various examples: an infinite-dimensional version of the Barndorff-Ni elsen–Shephard stochastic volatility model\, as well as a model involvin g self-exciting volatility.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Michèle Vanmaele (University of Ghent) DTSTART:20211105T100000Z DTEND:20211105T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/29 DESCRIPTION:Title: Mortality/Longevity Risk-Minimization with or without Securitization\nby Michèle Vanmaele (University of Ghent) as part of STAR seminars\n\n\nAbstract\nIn this talk we will address the risk-minimi zation problem\, with and without mortality securitization\,\nà la Föllm er–Sondermann for a large class of equity-linked mortality contracts whe n no\nmodel for the death time is specified. This framework includes situa tions in which the correlation\nbetween the market model and the time of d eath is arbitrary general\, and hence leads to the case of a\nmarket model where there are two levels of information—the public information\, whic h is generated\nby the financial assets\, and a larger flow of information that contains additional knowledge about\nthe death time of an insured. W e will derive the dynamics of the value processes of the mortality/longevi ty securities used for the securitization\, and decompose any mortality/lo ngevity liability into the sum of orthogonal risks by means of a risk basi s. Next\, we will quantify\, as explicitly as possible\, the effect of mor tality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtrati on. We will obtain \n risk-minimizing strategies with insurance securitiza tion by investing in stocks and one (or more) mortality/longevity derivati ves such as longevity bonds. \n\nThe talk is based on joint work with Tahi r Choull (University of Alberta)i and Catherine Daveloose (Ghent Universit y).\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Tugaut (Université Jean Monnet\, Saint-Etienne) DTSTART:20211109T121500Z DTEND:20211109T130000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/30 DESCRIPTION:by Julian Tugaut (Université Jean Monnet\, Saint-Etienne) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/30/ END:VEVENT BEGIN:VEVENT SUMMARY:1-day workshop (Multiple) DTSTART:20211112T080000Z DTEND:20211112T160000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/31 DESCRIPTION:Title: Recent Developments in Stochastics 2021\nby 1-day workshop (Multiple) as part of STAR seminars\n\n\nAbstract\nThe STAR rese arch seminar is replaced today by the 1.day workshop\nRecent Developments in Stochastics 2021\nFor information\, please visit\nhttps://www.mn.uio.no /math/english/research/projects/storm/events/conferences/recent-developmen ts-in-stochastics%281%29/index.html\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlo Sgarra (Politecnico di Milano) DTSTART:20211210T090000Z DTEND:20211210T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/32 DESCRIPTION:Title: Optimal Reinsurance Strategies in a Partially Observa ble Contagion Model\nby Carlo Sgarra (Politecnico di Milano) as part o f STAR seminars\n\n\nAbstract\nWe investigate the optimal reinsurance prob lem when the loss process exhibits jump clustering features and the insura nce company has restricted information about the loss process. We maximize expected exponential utility and show that an optimal solution exists. We provide the equation governing the dynamics of the (infinite-dimensional) filter and characterize the solution of the stochastic optimization probl em as the solution of a BSDE.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/32/ END:VEVENT BEGIN:VEVENT SUMMARY:2-days workshop (Multiple) DTSTART:20211125T070000Z DTEND:20211125T140000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/33 DESCRIPTION:Title: Rough path techniques in stochastic analysis and math ematical probability\nby 2-days workshop (Multiple) as part of STAR se minars\n\nAbstract: TBA\n\nPlease visit the dedicated webpage:\nhttps://ww w.mn.uio.no/math/english/research/projects/storm/events/conferences/rough- path-techniques-in-stochastic-analysis-and-m/rough-path-techniques-in-stoc hastic-analysis-and-m.html\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/33/ END:VEVENT BEGIN:VEVENT SUMMARY:2-days workshop (Multiple) DTSTART:20211126T070000Z DTEND:20211126T140000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/34 DESCRIPTION:Title: Rough path techniques in stochastic analysis and math ematical probability\nby 2-days workshop (Multiple) as part of STAR se minars\n\n\nAbstract\nPlease visit the dedicated webpage:\nhttps://sites.g oogle.com/view/rpisa2021/start\n\nhttps://www.mn.uio.no/math/english/resea rch/projects/storm/events/conferences/rough-path-techniques-in-stochastic- analysis-and-m/rough-path-techniques-in-stochastic-analysis-and-m.html\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Karbach (University of Amsterdam) DTSTART:20211210T100000Z DTEND:20211210T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/35 DESCRIPTION:Title: Positive multivariate CARMA processe\nby Sven Kar bach (University of Amsterdam) as part of STAR seminars\n\n\nAbstract\nIn this talk we discuss positivity of multivariate continuous-time autoregres sive moving-average (MCARMA) processes. In particular\, we introduce matri x valued MCARMA processes and derive sufficient and necessary conditions s uch that the processes leave the cone of positive semi-definite matrices i nvariant. MCARMA processes on the cone of positive semi-definite matrices can be used to model e.g. the instantaneous covariance process in multivar iate stochastic volatility models.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Lord (Radbrukne University) DTSTART:20220121T100000Z DTEND:20220121T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/36 DESCRIPTION:Title: GBM based exponential integrators\nby Gabriel Lor d (Radbrukne University) as part of STAR seminars\n\n\nAbstract\nWe introd uce a type of exponential time integrator which exploits linear terms in b oth the drift and diffusion for Stochastic Differential Equations (SDEs). We derive the scheme and show how it can be extended to general SDEs and d iscuss strong convergence. We initially examine strong convergence for glo bally Lipschitz drift and diffusion before introducing a tamed version. We illustrate the efficiency by considering some well-known SDE models. If time permits I will discuss weak convergence of these schemes.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaozhong Hu (University of Alberta) DTSTART:20220204T100000Z DTEND:20220204T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/37 DESCRIPTION:Title: Parameter estimation for threshold Ornstein-Uhlenbeck processes from discrete observations\nby Yaozhong Hu (University of A lberta) as part of STAR seminars\n\n\nAbstract\nAssuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants\, we shal l present the generalized moment estimators to estimate the parameters. The theoretical basis is the celebrated ergodic theorem. To use this theor em we need to find the explicit form of the invariant measure. With the sa mpling time step arbitrarily fixed\, we prove the strong consistency and a symptotic normality of our estimators as the sample size tends to infinity .\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Ramsay (University of Nebraska-Lincoln) DTSTART:20220218T100000Z DTEND:20220218T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/38 DESCRIPTION:Title: CANCELLED - Doubly Enhanced Medicaid Partnership Annu ities (DEMPANs): A New Tool for Providing Long Term Care to Retired U.S. S eniors in the Medicaid Penumbra\nby Colin Ramsay (University of Nebras ka-Lincoln) as part of STAR seminars\n\n\nAbstract\nCANCELLED - NEW DATE W ILL BE ANNOUNCED IN DUE TIME\n\n\nA major problem facing many U.S. retiree s is accessing and paying for long term care. The 2019 National Associatio n of Insurance Commissioners (NAIC) guide on long term care insurance esti mates that\, of the individuals living in the U.S. who reach age 65\, abou t 70% are expected to need some form of long term care at least once in th eir lifetime and about 35% are expected to enter a nursing home at least o nce in their lifetime. Although Medicare covers most of a U.S. retiree’s medical care\, Medicare does not ordinarily pay for long term care. U.S. retirees often can access long term care services via the Medicaid program \, which is a means-tested program geared to lower income Americans. But\, to quickly qualify for Medicaid\, many retirees take drastic steps such a s transferring their assets to family members. When access to long term ca re is not urgent and long term planning is an option\, most U.S. States ha ve developed so-called Partnership for Long Term Care (PLTC) Program insur ance policies that provide access to Medicaid services while sheltering so me or all of a retiree’s assets. In this paper\, we pro11 pose a hybrid annuity product called a doubly enhanced Medicaid Partnership annuity (DEM PAN) that combines an annuity with a long term care rider that is integrat ed within the framework of a qualified Partnership policy. (Outside the U. S.\, bundled retirement products similar to DEMPANs are called life-care a nnuities.) To analyze our DEMPANs\, we use a multi-state model of long ter m care with health states that are based on a retiree’s ability to perfo rm activities of daily living (ADLs)\, instrumental activities of daily li ving (IADLs)\, and cognitive ability. A significant contribution of this p aper is to explicitly model how the quality of long term care a retiree re ceives affects the retiree’s health state transition probabilities used in the multi-state model. As higher quality of care usually comes at a hig her cost but with better health outcomes\, we provided an example that exp lores an expected discounted utility maximizing retiree’s optimal choice of DEMPAN. Our example showed that it may be optimal for retirees who pur chase DEMPANs to buy average quality long term care. We hope DEMPANs fill a gap in the long term care market by providing an important tool for elde rcare planning for those in the Medicaid penumbra (i.e.\, in the middle an d lower-middle income classes). Retirees who purchase DEMPANs have the ben efits of an annuity\, private long term care\, Medicaid assistance with pa ying their long term care bills\, and some degree of asset protection from Medicaid estate recovery.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Detering (UC Santa Barbara) DTSTART:20220304T100000Z DTEND:20220304T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/39 DESCRIPTION:Title: When do you Stop Supporting your Bankrupt Subsidiary< /a>\nby Nils Detering (UC Santa Barbara) as part of STAR seminars\n\n\nAbs tract\nWe consider a network of bank holdings\, where every holding has tw o subsidiaries of different type. A subsidiary can trade with another hold ing's subsidiary of the same type. Holdings support their subsidiary up to a certain level when they would otherwise fail to honor their financial o bligations. We investigate the spread of contagion in this banking network when the number of bank holdings is large\, and find the final number of defaulted subsidiaries under different rules for the holding support. We a lso consider resilience of this multilayered network to small shocks. Our work sheds light onto the role that holding structures can play in the amp lification of financial stress. \nWe find that depending on the capitalis ation of the network\, a holding structure can be beneficial as compared t o smaller separated entities. In other instances it can be harmful and act ually increase contagion.\nWe illustrate our results in a numerical case s tudy and also determine the optimal level of holding support from a regula tor perspective.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Rosazza Gianin (University of Milano Bicocca) DTSTART:20220318T100000Z DTEND:20220318T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/40 DESCRIPTION:Title: Generalized PELVE and applications to risk measures\nby Emanuela Rosazza Gianin (University of Milano Bicocca) as part of S TAR seminars\n\n\nAbstract\nThe continuing evolution of insurance and bank ing regulation has\nraised interest in the calibration of different risk m easures associated\nwith suitable confidence levels. In particular\, Li an d Wang (2019)\nhave introduced a probability equivalent level (called PELV E) for the\nreplacement of Value at Risk with Conditional Value at Risk. \ nIn this talk\, we propose two alternative generalizations of PELVE (disto rted PELVE and generalized PELVE) by means of distortion functions in the former case\, while to more general pairs of risk measures in the latter. Conditions for the existence\nand uniqueness of distorted and generalized PELVE and additional properties for specific families of risk measures ar e discussed. \nA study of Generalized Pareto Distributions reveals\nan int eresting correspondence between PELVE and generalized PELVE\, and explores \ntheir relationship with the tail index. An empirical application\nillust rates the usefulness of (generalized) PELVE in characterizing tail behavio r\nnot only for individual asset returns\, but also for possible portfolio \ncombinations.\nBased on a joint work with Anna Maria Fiori.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Erlend Grong (University of Bergen) DTSTART:20220401T090000Z DTEND:20220401T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/41 DESCRIPTION:Title: Path space on sub-Riemannian manifolds\nby Erlend Grong (University of Bergen) as part of STAR seminars\n\n\nAbstract\nWe d iscuss how we can generalize the concept of Malliavin Calculus to the sett ing of a sub-Riemannian manifolds. We explain how concepts such as the Cam eron-Martin space\, the gradient and damped gradient of functions on path space can be understood in this setting. As an application\, we show how w e can obtain functional inequalities related to both a lower and upper bou nds for Ricci curvature. These results are from a joint work with Li-Juan Cheng and Anton Thalmaier.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/41/ END:VEVENT BEGIN:VEVENT SUMMARY:José Garrido (Concordia University Montreal) DTSTART:20220427T101500Z DTEND:20220427T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/42 DESCRIPTION:Title: Bridging epidemiological and actuarial models: the ca se of COVID-19\nby José Garrido (Concordia University Montreal) as pa rt of STAR seminars\n\n\nAbstract\nOur society's efforts to fight pandemic s rely heavily on our ability to understand\, model and predict the transm ission dynamics of infectious diseases. Compartmental models are among the most commonly used mathematical tools to explain reported infections and deaths. This collective book chapter offers a brief overview of basic comp artmental models as well as several actuarial applications\, ranging from product design and reserving of epidemic insurance\, to the projection of healthcare demand and the allocation of scarce resources. The intent is to bridge classical epidemiological models with actuarial and financial appl ications that provide healthcare coverage and utilise limited healthcare r esources during pandemics.\n\nAuthors: R. Feng (University of Illinois at Urbana--Champaign\, UIUC)\, J. Garrido (Concordia University)\, L. Jin\, L . Zhang (UIUC) and S-H. Loke (Central Washington University)\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo Abi Jaber (Université Paris 1 Panthéon-Sorbonne) DTSTART:20220506T090000Z DTEND:20220506T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/43 DESCRIPTION:Title: Quadratic Gaussian models: analytic expressions for p ricing and portfolio allocation\nby Eduardo Abi Jaber (Université Par is 1 Panthéon-Sorbonne) as part of STAR seminars\n\n\nAbstract\nStochasti c models based on Gaussian processes\, like fractional Brownian motion\, a re able to reproduce important stylized facts of financial markets such as rich autocorrelation structures\, persistence and roughness of sample pat hs. This is made possible by virtue of the flexibility introduced in the c hoice of the covariance function of the Gaussian process. The price to pay is that\, in general\, such models are no longer Markovian nor semimartin gales\, which limits their practical use. We derive explicit analytic expr essions for Fourier-Laplace transforms of quadratic functionals of Gaussia n processes. Such analytic expression can be approximated by closed form m atrix expressions stemming from Wishart distributions. \nWe highlight the applicability of such result in the context of rough volatility modeling: (i) fast pricing and calibration in the (rough) fractional Stein-Stein mo del\; (ii) explicit solutions for the Markowitz portfolio allocation probl em in a multivariate rough Stein—Stein model.\nBased on joint works with Enzo Miller and Huyên Pham.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Olena Tymoshenko (Kiev Polytechnique Institute) DTSTART:20220520T080000Z DTEND:20220520T090000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/44 DESCRIPTION:by Olena Tymoshenko (Kiev Polytechnique Institute) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Kjetil Røysland (University of Oslo) DTSTART:20220520T090000Z DTEND:20220520T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/45 DESCRIPTION:by Kjetil Røysland (University of Oslo) as part of STAR semin ars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220603T080000Z DTEND:20220603T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/46 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy process es Part I\nby Markus Riedle (Kings College London) as part of STAR sem inars\n\n\nAbstract\nCylindrical Lévy processes are a natural extension o f cylindrical Brownian motion which has been the standard model of random perturbations of partial differential equations and other models in infini te dimensions for the last 50 years. Here\, the attribute cylindrical refe rs to the fact that cylindrical Brownian motions are not classical stochas tic processes attaining values in the underlying space but are generalised objects. The reasons for the choice of cylindrical but not classical Brow nian motion can be found in the facts that there does not exist a classica l Brownian motion with independent components in an infinite dimensional H ilbert space\, and that cylindrical processes enable a very flexible model ling of random noise in time and space.\nIn this lecture series\, we brief ly present some aspects of the theory of cylindrical measures and cylindri cal random variables. We introduce cylindrical Lévy processes and present some specific examples in detail and discuss their relations to other mod els of random perturbations in the literature. We present a theory of stoc hastic integration with respect to cylindrical random variables\, which ca nnot rely on the classical approach\, as cylindrical Lévy processes do no t enjoy a semi-martingale decomposition. We finish this lecture series by investigating some specific models driven by cylindrical Lévy processes\, such as Ornstein-Uhlenbeck processes.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220614T090000Z DTEND:20220614T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/47 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy process es Part II\nby Markus Riedle (Kings College London) as part of STAR se minars\n\n\nAbstract\nCylindrical Lévy processes are a natural extension of cylindrical Brownian motion which has been the standard model of random perturbations of partial differential equations and other models in infin ite dimensions for the last 50 years. Here\, the attribute cylindrical ref ers to the fact that cylindrical Brownian motions are not classical stocha stic processes attaining values in the underlying space but are generalise d objects. The reasons for the choice of cylindrical but not classical Bro wnian motion can be found in the facts that there does not exist a classic al Brownian motion with independent components in an infinite dimensional Hilbert space\, and that cylindrical processes enable a very flexible mode lling of random noise in time and space.\nIn this lecture series\, we brie fly present some aspects of the theory of cylindrical measures and cylindr ical random variables. We introduce cylindrical Lévy processes and presen t some specific examples in detail and discuss their relations to other mo dels of random perturbations in the literature. We present a theory of sto chastic integration with respect to cylindrical random variables\, which c annot rely on the classical approach\, as cylindrical Lévy processes do n ot enjoy a semi-martingale decomposition. We finish this lecture series by investigating some specific models driven by cylindrical Lévy processes\ , such as Ornstein-Uhlenbeck processes.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220617T080000Z DTEND:20220617T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/48 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy process es Part III\nby Markus Riedle (Kings College London) as part of STAR s eminars\n\n\nAbstract\nCylindrical Lévy processes are a natural extension of cylindrical Brownian motion which has been the standard model of rando m perturbations of partial differential equations and other models in infi nite dimensions for the last 50 years. Here\, the attribute cylindrical re fers to the fact that cylindrical Brownian motions are not classical stoch astic processes attaining values in the underlying space but are generalis ed objects. The reasons for the choice of cylindrical but not classical Br ownian motion can be found in the facts that there does not exist a classi cal Brownian motion with independent components in an infinite dimensional Hilbert space\, and that cylindrical processes enable a very flexible mod elling of random noise in time and space.\nIn this lecture series\, we bri efly present some aspects of the theory of cylindrical measures and cylind rical random variables. We introduce cylindrical Lévy processes and prese nt some specific examples in detail and discuss their relations to other m odels of random perturbations in the literature. We present a theory of st ochastic integration with respect to cylindrical random variables\, which cannot rely on the classical approach\, as cylindrical Lévy processes do not enjoy a semi-martingale decomposition. We finish this lecture series b y investigating some specific models driven by cylindrical Lévy processes \, such as Ornstein-Uhlenbeck processes.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Péter Vékás (Corvinus University of Budapest) DTSTART:20220923T090000Z DTEND:20220923T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/49 DESCRIPTION:Title: AI in Longevity Risk Management: Improved Long-Term P rojections by Machine Learning\nby Péter Vékás (Corvinus University of Budapest) as part of STAR seminars\n\n\nAbstract\nWhile human mortalit y has decreased significantly since the beginning of the past century\, re sulting in unprecedented increases in human life expectancies\, several au thors have noted a historical pattern of diminishing mortality decline at relatively younger ages along with accelerating improvements among the eld erly. Li\, Lee and Gerland (2013) call this phenomenon the ’rotation’ of the age pattern of mortality decline. A somewhat simplistic explanation of this is that spectacular decreases in infant and childhood mortality r ates (e.g.\, due to widespread vaccination programs and improved child nut rition) are less and less possible\, while costly medical procedures to ex tend life at advanced ages are increasingly available.\nThe practical actu arial significance of the topic is that ignoring rotation in long-term mor tality forecasts may lead to a severe and systematic underestimation of th e old-aged population\, which exacerbates longevity risk and may lead to s erious adverse financial consequences for life and health insurers as well as pension schemes.\nThe popular model of Lee and Carter (1992) as well a s many other mortality forecasting techniques do not allow for rotation at all. To correct this shortcoming\, Li\, Lee and Gerland (2013) introduced a variant of the Lee–Carter model including rotation. This model extens ion assumes that the evolution of mortality improvement rates follows a pa rametric equation\, whose two parameters govern the speed of rotation and the level of life expectancy where the process begins.\nWe use age-specifi c mortality rates of all countries by gender from the Human Mortality Data base (HMD)\, and split the available time periods by country into a traini ng set spanning from the first available year up to 1990\, a validation se t from 1991 to 1999 and a test set containing all years after 1999. Instea d of fixed values of the two parameters mentioned in the previous paragrap h\, as suggested by Li\, Lee and Gerland (2013)\, we propose to treat them as hyperparameters and optimize them on the validation set\, as it is cus tomarily done in machine learning\, in order to improve long- term forecas ting performance. Additionally\, we propose deep neural networks specifica lly designed to capture the rotation of mortality decline in order to prod uce even more data-driven rotation schedules free of any prior assumptions \, and we tune the hyperparameters of the networks on the validation set. As a third candidate\, we also propose a generalized additive model involv ing the bivariate spline approximation of the residuals of the Lee–Carte r model. This approach is halfway between fully parametric models such as the variant of the Lee–Carter model including rotation and fully data-dr iven ones such as deep neural networks.\nWe use the test set to assess and compare the performance of the rotated variant of the Lee–Carter model including hyperparameter tuning\, the deep neural network capturing rotati on and the spline GAM approach. We will point out which approach works bes t in the long run in every country\, which countries are more or less pron e to rotation\, and how actual rotation schedules differ from the parametr ic form hypothesized by Li\, Lee and Gerland (2013).\nFinally\, we use our models to assess longevity risk in a pension scheme and point out the pot ential financial benefits of implementing our improved methods of capturin g rotation in mortality data\, and also elaborate on the potential impact of COVID-19 and how it is best incorporated into these models.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Knut Sølna (University of California\, Irvine) DTSTART:20221028T090000Z DTEND:20221028T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/50 DESCRIPTION:Title: Asymptotics with Rough and Multiscale Stochastic Vola tility\nby Knut Sølna (University of California\, Irvine) as part of STAR seminars\n\n\nAbstract\nWe discuss some stochastic volatility models used in mathematical finance. The stochastic volatility modeling involves multiscale frameworks and the asymptotic analysis of the associated stocha stic differential equations exploits separation of time scales. The asympt otic analysis leads to parsimonious expressions for pricing of various fin ancial instruments. Recent empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset a nd we present in particular results for so-called rough volatility models motivated by such observations.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasz Klimsiak (Nicolaus Copernicus University) DTSTART:20221129T100000Z DTEND:20221129T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/51 DESCRIPTION:Title: Non-semimartingale solutions to reflected BSDEs with applications to Dynkin games\nby Tomasz Klimsiak (Nicolaus Copernicus University) as part of STAR seminars\n\n\nAbstract\nt is well known that t he theory of Reflected BSDEs is well-posed under the Mokobodzki condition on the barriers L\,U. This is due to the fact that by the very definition of a solution to RBSDE\, its first component is a semimartingale that lies between the barriers - this is exactly the content of the (weak) Mokobodz ki condition. However\, there is an intimate connection between solutions of RBSDEs and value processes in Dynkin games and it is well known that in some instances the latter process is well defined even if Mokobodzki’s condition does not hold\, so the natural question arises whether such a pr ocess solves in a unique way certain backward SDE. Our goal is to extend t he notion of RBSDEs and provide the existence and uniqueness results to ob tain a one-to-one correspondence between solutions of RBSDEs and value pro cesses in nonlinear Dynkin games.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Saul Jacka (University of Warwick) DTSTART:20221214T100000Z DTEND:20221214T110000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/52 DESCRIPTION:Title: CANCELLED - Optimal Stopping and Technical Analysis\nby Saul Jacka (University of Warwick) as part of STAR seminars\n\n\nAb stract\nThe seminar is cancelled and postponed. New date will be announced .\n\nAbstract:\nTechnical Analysis is a collection of investment policies based on the history of price processes. It is widely used by institutiona l investors despite conflict with the Efficient Markets Hypothesis. In thi s talk we'll discuss a very general model of a stock price which is design ed to analyse the viability of a form of technical analysis known as the s upport and resistance line method.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Riedel (University of Bielefeld) DTSTART:20230315T121500Z DTEND:20230315T130000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/53 DESCRIPTION:Title: Approaches to Knightian Uncertainty in Finance and Ec onomics\nby Frank Riedel (University of Bielefeld) as part of STAR sem inars\n\n\nAbstract\nThe lecture reviews recent model of preferences unde r Knightian uncertainty. These approaches are closely related to attempts to quantify risk in finance. A particular focus will be on the so-called s mooth model\, an ambiguity-averse version of a second-order Bayesian Ansat z\, that goes back to Klibanoff\, Marinacci\, and Mukerji (Econometrica 2 005). We will study its axiomatic foundations and discuss the relationshi p of this approach with statistics\, in particular the issue of identifica tion of models (Denti\, Pomatto\, Econometrica 2022). Moreover\, we show how the smooth model is related to variational and coherent risk measures. The lecture will provide the necessary background for the lecture on Frid ay.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Riedel (University of Bielefeld) DTSTART:20230317T091500Z DTEND:20230317T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/54 DESCRIPTION:Title: Efficient Allocations under Ambiguous Model Uncertain ty\nby Frank Riedel (University of Bielefeld) as part of STAR seminars \n\n\nAbstract\nWe investigate consequences of model uncertainty (or ambig uity) on ex ante efficient allocations in an exchange economy. The ambigui ty we consider is embodied in the model uncertainty perceived by the decis ion maker: they are unsure what would be the appropriate probability measu re to apply to evaluate contingent consumption contingent plans and keep in consideration a set of alternative probabilistic laws. We study the c ase where the typical consumer in the economy is ambiguity-averse with smo oth ambiguity preferences and the set of priors P is point identified\, i .e.\, the true law p can be recovered empirically from observed events. Di fferently from the literature\, we allow for the case where the aggregate risk is ambiguous and agents are heterogeneously ambiguity averse. Our ana lysis addresses\, in particular\, the full range of set-ups where under ex pected utility the Pareto efficient consumption sharing rule is a linear f unction of the aggregate endowment. We identify systematic differences amb iguity aversion introduces to optimal sharing arrangements in these enviro nments and also characterize the representative consumer. Furthermore\, we investigate the implications for the state-price function\, in particular \, the effect of heterogeneity in ambiguity aversion.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Schroers (University of Bonn) DTSTART:20230421T090000Z DTEND:20230421T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/55 DESCRIPTION:by Dennis Schroers (University of Bonn) as part of STAR semina rs\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Rosazza-Gianin (University Bicocca-Milano) DTSTART:20230421T080000Z DTEND:20230421T090000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/56 DESCRIPTION:by Emanuela Rosazza-Gianin (University Bicocca-Milano) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Petersson (University of Oslo) DTSTART:20230428T090000Z DTEND:20230428T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/57 DESCRIPTION:by Andreas Petersson (University of Oslo) as part of STAR semi nars\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230329T110000Z DTEND:20230329T140000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/58 DESCRIPTION:Title: Signature methods in finance I\nby Christa Cuchie ro (University of Vienna) as part of STAR seminars\n\n\nAbstract\nSignatur e methods represent a non-parametric way for extracting characteristic fea tures from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in Econome trics and Mathematical Finance. Indeed\, signature based approaches allow for data-driven and thus more robust model selection mechanisms\, while fi rst principles like no arbitrage can still be easily guaranteed. \n\nIn th is course we shall focus on the use of signature as universal linear regre ssion basis of continuous functionals of paths for financial applications. \nWe first give an introduction to continuous rough paths and show how to embed continuous semimartingales into the rough path setting. Indeed our main focus lies on signature of semimartingales\, one of the main modeling tools in finance. By relying on the Stone-Weierstrass theorem we show how to prove the universal approximation property of linear functions of the signature in appropriate topologies on path space. To cover models with ju mps we shall additionally introduce the notion of cadlag rough paths\, Mar cus signature and its universal approximation properties in appropriate Sk orokhod topologies. \n\nIn the financial applications that we have in mind one key quantity that one needs to compute is the expected signature of s ome underlying process. Surprisingly this can be achieved for generic clas ses of jump diffusions (with possibly path dependent characteristics) via techniques from affine and polynomial processes. More precisely\, we show how the signature process of these jump diffusions can be embedded in the framework of affine and polynomial processes. These classes of processes h ave been -- due to their tractability -- the dominating process class prio r to the new era of highly over-parametrized dynamic models. Following thi s line we obtain that the infinite dimensional Feynman Kac PIDE of the sig nature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series exp ansions for the expected signature and the Fourier-Laplace transform. \n\n In terms of financial applications\, we shall treat two main topics: stoch astic portfolio theory and signature based asset price models. \n\nIn the context of stochastic portfolio theory we introduce a novel class of portf olios which we call linear path-functional portfolios. These are portfolio s which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals of an underlying semimartingale. As main example for such feature maps we co nsider signature of the (ranked) market weights. Relying on the universal approximation theorem we show that every continuous (possibly path-depend ent) portfolio function of the market weights can be uniformly approximate d by signature portfolios. Besides these universality features\, the main numerical advantage lies in the fact that several optimization tasks like maximizing expected logarithmic utility or mean-variance optimization with in the class of linear path-functional portfolios reduces to a convex quad ratic optimization problem\, thus making it computationally highly tractab le. We apply our method to real market data and show generic out-performan ce on out-of-sample data even under transaction costs. \n\nIn view of asse t price models we consider a stochastic volatility model where the dynamic s of the volatility are described by linear functions of the (time extende d) signature of a primary underlying process\, which is supposed to be som e multidimensional continuous semimartingale. Under the additional assumpt ion that this primary process is of polynomial type\, we obtain closed for m expressions for the VIX squared\, exploiting the fact that the truncated signature of a polynomial process is again a polynomial process. Adding t o such a primary process the Brownian motion driving the stock price\, all ows then to express both the log-price and the VIX squared as linear funct ions of the signature of the corresponding augmented process. This feature can then be efficiently used for pricing and calibration purposes. Indee d\, as the signature samples can be easily precomputed\, the calibration t ask can be split into an offline sampling and a standard optimization. Fo r both the SPX and VIX options we obtain highly accurate calibration resul ts\, showing that this model class allows to solve the joint calibration p roblem without adding jumps or rough volatility.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230331T080000Z DTEND:20230331T100000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/59 DESCRIPTION:Title: Signature methods in finance III\nby Christa Cuch iero (University of Vienna) as part of STAR seminars\n\n\nAbstract\nSignat ure methods represent a non-parametric way for extracting characteristic f eatures from time series data which is essential in machine learning tasks . This explains why these techniques become more and more popular in Econo metrics and Mathematical Finance. Indeed\, signature based approaches allo w for data-driven and thus more robust model selection mechanisms\, while first principles like no arbitrage can still be easily guaranteed. \n\nIn this course we shall focus on the use of signature as universal linear reg ression basis of continuous functionals of paths for financial application s. \nWe first give an introduction to continuous rough paths and show how to embed continuous semimartingales into the rough path setting. Indeed ou r main focus lies on signature of semimartingales\, one of the main modeli ng tools in finance. By relying on the Stone-Weierstrass theorem we show h ow to prove the universal approximation property of linear functions of th e signature in appropriate topologies on path space. To cover models with jumps we shall additionally introduce the notion of cadlag rough paths\, M arcus signature and its universal approximation properties in appropriate Skorokhod topologies. \n\nIn the financial applications that we have in mi nd one key quantity that one needs to compute is the expected signature of some underlying process. Surprisingly this can be achieved for generic cl asses of jump diffusions (with possibly path dependent characteristics) vi a techniques from affine and polynomial processes. More precisely\, we sho w how the signature process of these jump diffusions can be embedded in th e framework of affine and polynomial processes. These classes of processes have been -- due to their tractability -- the dominating process class pr ior to the new era of highly over-parametrized dynamic models. Following t his line we obtain that the infinite dimensional Feynman Kac PIDE of the s ignature process can generically be reduced to an infinite dimensional OD E either of Riccati or linear type. This then allows to get power series e xpansions for the expected signature and the Fourier-Laplace transform. \n \nIn terms of financial applications\, we shall treat two main topics: sto chastic portfolio theory and signature based asset price models. \n\nIn th e context of stochastic portfolio theory we introduce a novel class of por tfolios which we call linear path-functional portfolios. These are portfol ios which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals of an underlying semimartingale. As main example for such feature maps we consider signature of the (ranked) market weights. Relying on the universa l approximation theorem we show that every continuous (possibly path-depe ndent) portfolio function of the market weights can be uniformly approxima ted by signature portfolios. Besides these universality features\, the mai n numerical advantage lies in the fact that several optimization tasks lik e maximizing expected logarithmic utility or mean-variance optimization wi thin the class of linear path-functional portfolios reduces to a convex qu adratic optimization problem\, thus making it computationally highly tract able. We apply our method to real market data and show generic out-perform ance on out-of-sample data even under transaction costs. \n\nIn view of as set price models we consider a stochastic volatility model where the dynam ics of the volatility are described by linear functions of the (time exten ded) signature of a primary underlying process\, which is supposed to be s ome multidimensional continuous semimartingale. Under the additional assum ption that this primary process is of polynomial type\, we obtain closed f orm expressions for the VIX squared\, exploiting the fact that the truncat ed signature of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, a llows then to express both the log-price and the VIX squared as linear fun ctions of the signature of the corresponding augmented process. This featu re can then be efficiently used for pricing and calibration purposes. Ind eed\, as the signature samples can be easily precomputed\, the calibration task can be split into an offline sampling and a standard optimization. For both the SPX and VIX options we obtain highly accurate calibration res ults\, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230330T110000Z DTEND:20230330T140000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/60 DESCRIPTION:Title: Signature methods in finance II\nby Christa Cuchi ero (University of Vienna) as part of STAR seminars\n\n\nAbstract\nSignatu re methods represent a non-parametric way for extracting characteristic fe atures from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in Econom etrics and Mathematical Finance. Indeed\, signature based approaches allow for data-driven and thus more robust model selection mechanisms\, while f irst principles like no arbitrage can still be easily guaranteed. \n\nIn t his course we shall focus on the use of signature as universal linear regr ession basis of continuous functionals of paths for financial applications . \nWe first give an introduction to continuous rough paths and show how t o embed continuous semimartingales into the rough path setting. Indeed our main focus lies on signature of semimartingales\, one of the main modelin g tools in finance. By relying on the Stone-Weierstrass theorem we show ho w to prove the universal approximation property of linear functions of the signature in appropriate topologies on path space. To cover models with j umps we shall additionally introduce the notion of cadlag rough paths\, Ma rcus signature and its universal approximation properties in appropriate S korokhod topologies. \n\nIn the financial applications that we have in min d one key quantity that one needs to compute is the expected signature of some underlying process. Surprisingly this can be achieved for generic cla sses of jump diffusions (with possibly path dependent characteristics) via techniques from affine and polynomial processes. More precisely\, we show how the signature process of these jump diffusions can be embedded in the framework of affine and polynomial processes. These classes of processes have been -- due to their tractability -- the dominating process class pri or to the new era of highly over-parametrized dynamic models. Following th is line we obtain that the infinite dimensional Feynman Kac PIDE of the si gnature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series ex pansions for the expected signature and the Fourier-Laplace transform. \n\ nIn terms of financial applications\, we shall treat two main topics: stoc hastic portfolio theory and signature based asset price models. \n\nIn the context of stochastic portfolio theory we introduce a novel class of port folios which we call linear path-functional portfolios. These are portfoli os which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals o f an underlying semimartingale. As main example for such feature maps we c onsider signature of the (ranked) market weights. Relying on the universal approximation theorem we show that every continuous (possibly path-depen dent) portfolio function of the market weights can be uniformly approximat ed by signature portfolios. Besides these universality features\, the main numerical advantage lies in the fact that several optimization tasks like maximizing expected logarithmic utility or mean-variance optimization wit hin the class of linear path-functional portfolios reduces to a convex qua dratic optimization problem\, thus making it computationally highly tracta ble. We apply our method to real market data and show generic out-performa nce on out-of-sample data even under transaction costs. \n\nIn view of ass et price models we consider a stochastic volatility model where the dynami cs of the volatility are described by linear functions of the (time extend ed) signature of a primary underlying process\, which is supposed to be so me multidimensional continuous semimartingale. Under the additional assump tion that this primary process is of polynomial type\, we obtain closed fo rm expressions for the VIX squared\, exploiting the fact that the truncate d signature of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, al lows then to express both the log-price and the VIX squared as linear func tions of the signature of the corresponding augmented process. This featur e can then be efficiently used for pricing and calibration purposes. Inde ed\, as the signature samples can be easily precomputed\, the calibration task can be split into an offline sampling and a standard optimization. F or both the SPX and VIX options we obtain highly accurate calibration resu lts\, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230331T110000Z DTEND:20230331T130000Z DTSTAMP:20260404T095626Z UID:STochastics_And_Risk/61 DESCRIPTION:Title: Signature methods in finance IV\nby Christa Cuchi ero (University of Vienna) as part of STAR seminars\n\n\nAbstract\nSignatu re methods represent a non-parametric way for extracting characteristic fe atures from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in Econom etrics and Mathematical Finance. Indeed\, signature based approaches allow for data-driven and thus more robust model selection mechanisms\, while f irst principles like no arbitrage can still be easily guaranteed. \n\nIn t his course we shall focus on the use of signature as universal linear regr ession basis of continuous functionals of paths for financial applications . \nWe first give an introduction to continuous rough paths and show how t o embed continuous semimartingales into the rough path setting. Indeed our main focus lies on signature of semimartingales\, one of the main modelin g tools in finance. By relying on the Stone-Weierstrass theorem we show ho w to prove the universal approximation property of linear functions of the signature in appropriate topologies on path space. To cover models with j umps we shall additionally introduce the notion of cadlag rough paths\, Ma rcus signature and its universal approximation properties in appropriate S korokhod topologies. \n\nIn the financial applications that we have in min d one key quantity that one needs to compute is the expected signature of some underlying process. Surprisingly this can be achieved for generic cla sses of jump diffusions (with possibly path dependent characteristics) via techniques from affine and polynomial processes. More precisely\, we show how the signature process of these jump diffusions can be embedded in the framework of affine and polynomial processes. These classes of processes have been -- due to their tractability -- the dominating process class pri or to the new era of highly over-parametrized dynamic models. Following th is line we obtain that the infinite dimensional Feynman Kac PIDE of the si gnature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series ex pansions for the expected signature and the Fourier-Laplace transform. \n\ nIn terms of financial applications\, we shall treat two main topics: stoc hastic portfolio theory and signature based asset price models. \n\nIn the context of stochastic portfolio theory we introduce a novel class of port folios which we call linear path-functional portfolios. These are portfoli os which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals o f an underlying semimartingale. As main example for such feature maps we c onsider signature of the (ranked) market weights. Relying on the universal approximation theorem we show that every continuous (possibly path-depen dent) portfolio function of the market weights can be uniformly approximat ed by signature portfolios. Besides these universality features\, the main numerical advantage lies in the fact that several optimization tasks like maximizing expected logarithmic utility or mean-variance optimization wit hin the class of linear path-functional portfolios reduces to a convex qua dratic optimization problem\, thus making it computationally highly tracta ble. We apply our method to real market data and show generic out-performa nce on out-of-sample data even under transaction costs. \n\nIn view of ass et price models we consider a stochastic volatility model where the dynami cs of the volatility are described by linear functions of the (time extend ed) signature of a primary underlying process\, which is supposed to be so me multidimensional continuous semimartingale. Under the additional assump tion that this primary process is of polynomial type\, we obtain closed fo rm expressions for the VIX squared\, exploiting the fact that the truncate d signature of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, al lows then to express both the log-price and the VIX squared as linear func tions of the signature of the corresponding augmented process. This featur e can then be efficiently used for pricing and calibration purposes. Inde ed\, as the signature samples can be easily precomputed\, the calibration task can be split into an offline sampling and a standard optimization. F or both the SPX and VIX options we obtain highly accurate calibration resu lts\, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://stable.researchseminars.org/talk/STochastics_And_Risk/61/ END:VEVENT END:VCALENDAR