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evenements:seminaireproba-math-fi [2019/05/03 11:37]
Valérie Picot
evenements:seminaireproba-math-fi [2019/11/04 13:23] (current)
Valérie Picot
Line 4: Line 4:
 Cliquer [[:​contact|ici]] pour plus d'​informations sur les moyens d'​accès. \\ 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__ :** **__Exposés de l'​année 2019__ :**
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 +**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).
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 +**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//
 +++ 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.
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 +**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.
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 **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)// **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)//
evenements/seminaireproba-math-fi.1556876266.txt.gz · Last modified: 2019/05/03 11:37 by Valérie Picot

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