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--- evenements:seminaireproba-math-fi [2019/04/08 20:03]
Valérie Picot
+++ evenements:seminaireproba-math-fi [2019/10/14 08:36] (current)
Valérie Picot
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 Cliquer [[:contact|ici]] pour plus d'informations sur les moyens d'accès. \\
-__Contact__ : Etienne Chevalier, Dasha Loukianova, Sergio Pulido \\
+__Contact__ : Christophe Profeta, Sergio Pulido, Abass Sagna \\
 **__Exposés de l'année 2019__ :**
+**17 octobre à 14h00 :** <color #088A85> Alexandre Veretennikov</color>  (University of Leeds)  //  On McKean-Vlasov stochastic equations//
+++ Voir résumé |  \\Weak existence will be shown for a class of McKean-Vlasov equations. Specifically results will be presented on: (a) existence for bounded Borel coefficients with non-degenerate diffusion (the class of coefficients is a bit wider than the standard linear coefficient dependence of the measure); (b) existence for unbounded Borel coefficients under linear growth given that for bounded ones existence is known; (c) existence for non-symmetric (& still non-degenerate) diffusions. In addition some results on strong existence and on weak and strong uniqueness will be stated.
+++
+**2 octobre à 14h00 :** <color #088A85> Sergio Pulido Nino </color>  (ENSIIE/LaMME)  //  Stochastic Volterra equations//
+++ Voir résumé |  \\We obtain general weak existence and stability results for Stochastic Convolution Equations (SVEs) with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. The motivation to study SVEs comes from the literature on rough volatility models. Our approach relies on weak convergence in Lp spaces. The main tools are new a priori estimates on Sobolev-Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit of classical martingale problem theory. To illustrate the applicability of our results, we consider scaling limits of nonlinear Hawkes processes and approximations of stochastic Volterra processes by Markovian semimartingales.
+++
+**26 septembre à 14h00 :** <color #088A85> Andrew Soane </color>  (University of Cape Town)  //  Optimal stopping with an enlarged filtration with an application to the Brownian Bridge//
+++ Voir résumé |  \\This talk will give an overview of the enlargement of filtration, focusing on the tools developed for its application, as well as a brief overview of optimal stopping problems from a Martingale perspective. We will then prove a relationship between the Snell envelope in the enlarged filtration and a parameterised Snell envelope in the reference filtration. Using this relationship we will then derive the optimal stopping value of a Brownian bridge, confirmed by results in the literature.
+++
+**16 mai à 14h00 :** <color #088A85> Aurélien  Alfonsi </color>  (  Ecole des Ponts ParisTech)  //   Approximation of OT problems with marginal moments contraints (Joint work with Rafaëll Coyaud, Virginie Ehrlacher and Damiano Lombardi)//
+++ Voir résumé |  \\Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some moment constraints. Using Tchakaloff's theorem, we show that the Moment Constrained Optimal Transport problem (MCOT) is achieved by a finite discrete measure. Interestingly, for multimarginal OT problems, the number of points weighted by this measure scales linearly with the number of marginal laws, which is encouraging to bypass the curse of dimension. This approximation method is also relevant for Martingale OT problems. We show the convergence of the MCOT problem toward the corresponding OT problem. In some fundamental cases, we obtain rates of convergence in $O(1/n)$ or $O(1/n^2)$ where $n$ is the number of moments, which illustrates the role of the moment functions. Last, we present algorithms exploiting that the MCOT is reached by a finite discrete measure and provide numerical examples of approximations..
+++
+**18 avril à 14h00 :** <color #088A85> Roxana Dumitrescu </color>  (King's College London)  //  Mean-field games of optimal stopping: a relaxed solution approach//
+++ Voir résumé |  \\We consider the mean-field game where each agent determines the optimal time to exit the game by solving anoptimal stopping problem with reward function depending on the density of the state processes of agents still present in thegame. We place ourselves in the framework of relaxed optimal stopping, which amounts to looking for the optimal occupationmeasure of the stopper rather than the optimal stopping time. This framework allows us to prove the existence of the relaxedNash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions. Further, weprove a rigorous relation between relaxed Nash equilibria and the notion of mixed solutions introduced in earlier works on thesubject, and provide a criterion, under which the optimal strategies are pure strategies, that is, behave in a similar way tostopping times. Finally, we present a numerical method for computing the equilibrium in the case of potential games and showits convergence (joint work with  Peter Tankov and G. Bouveret).
+++
 **11 avril à 14h00 :** <color #088A85> Caroline Hillairet </color>  (ENSAE) //  Aggregation of  heterogeneous  consistent progressive utilities//

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