BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fabian Harang (University of Oslo) DTSTART:20200507T090000Z DTEND:20200507T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/1 DESCRIPTION:Title: Deterministic regularization by noise\nby Fabian Harang (Un iversity of Oslo) as part of Spring with STORM\n\nLecture held in Zoom vir tual room.\n\nAbstract\nIn this talk we will discuss the concept of regula rization by noise in SDEs from a pathwise point of view. Together with Pro f. Nicolas Perkowski at Humboldt University we recently proved that soluti ons to ODE's perturbed by a particular irregular (but continuous) path exi sts uniquely\, even when the drift vector field of the ODE is only a Scwar tz distribution. Moreover\, the flow associated to such perturbed ODE is i nfinitely differentiable. This gives insight into the powerful effect that noise may have on certain equations. We will also discuss an ongoing exte nsion of these results to the regularization by noise towards PDE/SPDEs. By this we mean that we consider an a-priori ill-posed non-linear PDE/SPDE \, and show that by perturbation of a sufficiently irregular path\, one ob tains well posedness of such equations.\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Giordano (University of Oslo) DTSTART:20200515T090000Z DTEND:20200515T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/2 DESCRIPTION:Title: Lifting of Volterra processes: optimal control and HJB equation s\nby Michele Giordano (University of Oslo) as part of Spring with STO RM\n\nLecture held in Zoom virtual room.\n\nAbstract\nIn this talk we pres ent a new approach to solve an optimization problem with Volterra dynamics driven by a Brownian motion. Thanks to a lift of the original problem to an infinite dimension Banach space\, we are able to recover some Markovian properties\, which in turn allow us to recover the HJB equations for the lifted problem.\nWith this approach we are thus able to solve the original Volterra optimization problem with a "classical" HJB approach.\nJoint wor k with Giulia di Nunno\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernt Øksendal (University of Oslo) DTSTART:20200520T090000Z DTEND:20200520T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/3 DESCRIPTION:Title: Optimal control of SPDEs with space interactions\nby Bernt Øksendal (University of Oslo) as part of Spring with STORM\n\nLecture hel d in Zoom virtual room.\n\nAbstract\nWe consider optimal control of a new type of stochastic partial differential equations (SPDEs)\, in which the d ynamics of the system state at a point also depends on the space-mean of v alues at neighbouring points. This is a model with many applications\, e.g . to population growth studies and epidemiology.\nBoth sufficient and nece ssary maximum principles for the optimal control of such systems are prove d. We also prove the existence and uniqueness of solutions of such equatio ns. As an illustration\, we apply the results to an optimal harvesting pro blem from a population whose density is modelled as a space-mean stochasti c reaction-diffusion equation.\nThe talk is based on joint works with Naci ra Agram and Astrid Hilbert\, Linnaeus University (LNU)\, Växjö\, Sweden \n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Silvia Lavagnini (University of Oslo) DTSTART:20200529T090000Z DTEND:20200529T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/4 DESCRIPTION:Title: Accuracy of deep learning in calibrating HJM forward curves \nby Silvia Lavagnini (University of Oslo) as part of Spring with STORM\n\ nLecture held in Zoom virtual room.\n\nAbstract\nWe price European-style o ptions written on forward contracts in the commodity market\, which we mod el with a state-dependent infinite-dimensional Heath-Jarrow-Morton (HJM) a pproach. We introduce a new volatility operator which maps the square inte grable noise into the Filipovi{\\'{c}} space of forward curves\, and we sp ecify a deterministic parametrized version of it. We train a neural networ k to approximate the option price as a function of the model parameters. W e then use it to calibrate the HJM parameters starting from (simulated) op tions market data. Finally we introduce a new loss function taking into ac count bid and ask prices\, providing a solution to the liquidity problem. A key issue discovered is that the trained neural network might be non-inj ective\, which could potentially lead to poor accuracy in calibrating the forward curve parameters\, even when showing high degree of accuracy in re covering the prices. This implies that the original meaning of the model p arameters gets somehow lost in the approximation step.\nThis is a joint wo rk with Fred Espen Benth (UiO) and Nils Detering (UCSB).\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Rosazza-Gianin (University of Milano Bicocca) DTSTART:20200603T090000Z DTEND:20200603T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/5 DESCRIPTION:Title: Capital allocation rules and acceptance sets\nby Emanuela R osazza-Gianin (University of Milano Bicocca) as part of Spring with STORM\ n\nLecture held in Zoom virtual room.\n\nAbstract\nIn the literature\, cap ital allocation problems are classically studied and associated to risk me asures. The aim of this talk is to introduce a new approach to face capita l allocation problems from the perspective of acceptance sets\, by definin g the family of sub-acceptance sets.\nWe study the relations between the n otions of sub-acceptability and acceptability of a risky position as well as their impact on capital allocation rules\; in this context\, indeed\, c apital allocation rules are interpretable as tools for assessing the contr ibution of a sub-portfolio to a given portfolio in terms of acceptability instead of necessarily involving a risk measure.\nFurthermore\, we investi gate under which conditions on a capital allocation rule a representation of an acceptance set holds in terms of the capital allocation rule itself in quite a general (convex\, quasiconvex\, S-additive) framework.\nFinally \, we investigate the correspondence between properties at the level of ca pital allocation rules and those at the level of sub-acceptance families.\ nThis talk is based on a joint work with Gabriele Canna and Francesca Cent rone.\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Yurchenko-Tytarenko (University of Oslo) DTSTART:20200612T090000Z DTEND:20200612T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/6 DESCRIPTION:Title: Sandwiched processes driven by Hölder noises\nby Anton Yur chenko-Tytarenko (University of Oslo) as part of Spring with STORM\n\n\nAb stract\nWe study a stochastic differential equation with an unbounded drif t and general Hölder continuous noise of an arbitrary order. The correspo nding equation turns out to have a unique solution that\, depending on a p articular shape of the drift\, either stays above some continuous function or has continuous upper and lower bounds. Under some additional assumptio ns on the noise\, we prove that the solution has moments of all orders. Ad ditionally\, numeric schemes for the solution are considered.\nAs illustra tions of our approach\, generalised CIR and CEV processes will be discusse d.\nThis talk is based on joint work with Giulia Di Nunno and Yuliya Mishu ra.\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/6/ END:VEVENT BEGIN:VEVENT SUMMARY:José Manuel Corcuera (University of Barcelona) DTSTART:20200617T090000Z DTEND:20200617T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/7 DESCRIPTION:Title: Path-dependent Kyle equilibrium model\nby José Manuel Corc uera (University of Barcelona) as part of Spring with STORM\n\n\nAbstract\ nKyle model is a classic model to explain the formation of prices\nin a fi nancial market. It is assumed that prices increase with the total\ndemand of the stock and market makers provide liquidity in the market and\nfix th e prices in a competitive way. The demand comes from noise traders and\nit s is assumed the presence of an informed trader who knows the liquidation\ nvalue of the stock. This informed trader tries to optimize their strategy .\nWhen all the actors are satisfied then we say that we have an equilibri um.\nDifferent kind of equilibriums have been obtained under the assumptio n that\nprices depend on the spot value of the total demand or a particula r\npath-dependence. In this work\, inspired by the functional It\\^{o} cal culus\,\nwe study the equilibrium when prices are a functional of the path of the\naggregate demand in a very general form. We consider the case whe n the\ninformed trader is risk neutral as well as the risk-averse case.\n\ nThis is joint work with Giulia di Nunno and Jos\\'{e} Fajardo who sadly\n passed away this third of May.\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Schoers (University of Oslo) DTSTART:20200626T090000Z DTEND:20200626T100000Z DTSTAMP:20260404T095135Z UID:SpringSTORM/8 DESCRIPTION:Title: Copulas and Sklar's theorem in infinite dimensions\nby Denn is Schoers (University of Oslo) as part of Spring with STORM\n\nAbstract: TBA\n\nCopulas describe statistical dependence between the components of m ultivariate random variables in full generality by virtue of Sklar’s the orem. Although they are used and defined for certain infinite dimensional objects (e.g. Gaussian processes\, Markov processes or infinite dimensiona l Archimedean copulas) there is no prevalent notion of a copula as an infi nite dimensional law that unifies these concepts. To this end we define co pulas as probability measures on product spaces and prove Sklar’s theore m in this general setting.\nAfterwards we use this result on Banach spaces to construct cylindrical probability measures with predefined marginals a nd underlying copula. This induces the functional analytic problem of find ing criteria in which cases the obtained cylindrical law induces a real pr obability measure\, which is in general difficult to decide. We solve this problem in the p-Wasserstein space on the space of p-summable sequences ( in- cluding separable Hilbert spaces) and show that copulas effectively so lve a restricted optimal coupling problem.\nThis is joint work with Fred E spen Benth and Giulia Di Nunno\n LOCATION:https://stable.researchseminars.org/talk/SpringSTORM/8/ END:VEVENT END:VCALENDAR