arXiv subjects

Habiba Knani

Publications and source records attributed to Habiba Knani.

2 recordsLinked to original sources

arXiv2020

Partial differential equations associated to non linear backward stochastic differential equations with Gaussian Volterra processes

In this paper, we generalize to Gaussian Volterra processes the existence and uniqueness of solutions for a class of non linear backward stochastic differential equations (BSDE) and we establish the relation between the non linear BSDE and the partial differential equation (PDE). A comparison theorem for the solution of the BSDE is proved and the continuity of its law is studied.

math.PR↗

arXiv2019

Linear Backward Stochastic Differential Equations with Gaussian Volterra processes

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional brownian motion and the multifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a linear second order partial differential equation with terminal condition whose solution is given by a Feynman-Kac type formula. An application to self-financing trading strategies is discussed.

math.PR↗