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--- evenements:seminaireproba-math-fi [2019/03/19 13:03]
Valérie Picot
+++ evenements:seminaireproba-math-fi [2019/04/18 08:34]
Valérie Picot
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 **__Exposés de l'année 2019__ :**
+**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//
+++ Voir résumé |  \\We aim  to describe globally the behavior and preferences of heterogeneous agents. Our starting point is the aggregate wealth of a given economy, with a given repartition of the wealth among investors, which is not necessarily Pareto optimal. We propose a construction of an aggregate forward utility, market consistent,that aggregates the marginal utility of the heterogeneous agents. This construction is based on the aggregation of the pricing kernels of each investor. As an application we analyze the impact of the heterogeneity and of the wealth market on the yield curve.
+Joint work with Nicole El Karoui et Mohamed Mrad.
+++
+**4 avril à 14h00 :** <color #088A85> Xiaolu Tan </color>  (Université Paris-Dauphine) //  From Martingale Optimal Transport to McKean-Vlasov Control Problems//
+++ Voir résumé |  \\The Martingale Optimal Transport (MOT) problem consists in maximizing a reward value among a class of martingales with given marginal distributions. It is motivated by its application in finance to obtain the no-arbitrage price bounds of derivative options in a data calibrated market. We consider a class of MOT problems and show how it could be related to a McKean-Vlasov (mean-field) control problem, which is a large population control problem. We then study the dynamic programming principle and the numerical approximation of the McKean-Vlasov control problem.
+++
+**4 avril à 15h00 :** <color #088A85> Ahmed Kebaier </color>  (Université Paris 13) // Non-asymptotic error bounds for The Multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient//
+++ Voir résumé |  \\In this work, we are interested in deriving non-asymptotic error bounds for the multilevel Monte Carlo method. As a first step, we deal with the explicit Euler discretization of stochastic differential equations with a constant diffusion coefficient. We prove that, as long as the deviation is below an explicit threshold, a Gaussian-type concentration inequality optimal in terms of the variance holds for the multilevel estimator. To do so, we use the Clark-Ocone representation formula and derive bounds for the moment generating functions of the squared difference between a crude Euler scheme and a finer one and of the squared difference of their Malliavin derivatives.
+++
 **28 mars à 14h00 :** <color #088A85> Carl Graham </color>  (Ecole Polytechnique) //  Théorèmes limites pour un processus de Hawkes avec auto excitation et inhibition à portée bornée//

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