backward stochastic differential equations driven by both standard and fractional Brownian motions with time deplayed generators

Abstract

This paper deals with a class of backward stochastic differential equations driven by both standard and fractional Brownian motions with time deplayed generators. In this type of equation, a generator at time $t$ can depend on the values of a solution in the past, weighted with a time delay function, for instance, of the moving average type. We establish an existence and uniqueness result of solutions for a sufficiently small time horizon or for a sufficiently small Lipschitz constant of a generator.