Delay BSDEs driven by fractional Brownian motion

Abstract This paper deals with a class of delay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also on the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is a divergence-type integral.