Séminaire MODAL'X : Kossi Gnameho (Modal'X)

Résumé : Backward stochastic differential equations (BSDEs) have been extensively studied in stochastic optimal control theory, mathematical finance, and insurance. Solving a BSDE consists of finding a pair of adapted processes (Y,Z) with respect to a given filtration that satisfy appropriate integrability conditions. In high dimensions, despite recent advances driven by artificial intelligence, deriving consistent numerical estimators for these stochastic equations remains a challenging task, particularly for the computation of the local martingale integrand, which is closely related to the Malliavin derivative. In this work, deep neural networks are leveraged to construct consistent numerical estimators for solving these equations based on chaos expansions. Numerical experiments are presented to illustrate the performance of the proposed approach.