Séminaire MODAL'X : Habiba Knani (MODAL'X, Université Paris Nanterre)

Résumé : In this talk we treat the backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Itoˆ formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. In the second part we treat the non-linear BSDE driven by the same class of Gaussian Volterra processes. The main result is the existence and uniqueness of the solution in a space of regular functionals of the Volterra process.