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--- evenements:seminaireproba-math-fi [2019/10/02 08:15]
Valérie Picot
+++ evenements:seminaireproba-math-fi [2019/11/04 13:23]
Valérie Picot
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 **__Exposés de l'année 2019__ :**
+**7 novembre à 14h00 :** <color #088A85> Lokmane Abbas Turki</color>(Sorbonne Universités - Paris 6)  //  Conditionnal Monte Carlo Learning for diffusions//
+++ Voir résumé |  \\We present a new algorithm based on One-Layered Nested Monte Carlo (1NMC) to simulate functionals $U$ of a Markov process $X$. The main originality of the proposed method comes from the fact that it provides a recipe to simulate $U_{t\geq s}$ conditionally on $X_{s}$. This recipe can be used for a large number of situations including: Backward Stochastic Differential Equations (BSDEs), Reflected BSDEs (RBSDEs), risk measures and beyond. In contrast to previous works, our contribution is based on a judicious combination between regression and 1NMC used for localization purpose. The generality, the stability and the iterative nature of this algorithm, even in high dimension, make its strength. It is of course heavier than a straight Monte Carlo (MC), however it is far more accurate to simulate quantities that are almost impossible to simulate with MC. Indeed, using the double layer of trajectories, we explain how to estimate and control the bias propagation. With this double layer structure, it is also possible to adjust the variance for a better description of tail events. Moreover, the parallel suitability of 1NMC makes it feasible in a reasonable computing time. This presentation explains this algorithm and details error estimates. We also provide various numerical examples with a dimension equal to 100 that are executed in few minutes on one Graphics Processing Unit (GPU).
+++
+**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.
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 **2 octobre à 14h00 :** <color #088A85> Sergio Pulido Nino </color>  (ENSIIE/LaMME)  //  Stochastic Volterra equations//

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