Wellposedness of anticipated BSDEs with quadratic growth and unbounded terminal value

Abstract

In this paper, we investigate a class of anticipated backward stochastic differential equations (ABSDEs) with quadratic growth and unbounded terminal conditions. ABSDEs give us a duality with stochastic optimal control problems with delay. On the other hand, quadratic ABSDEs can be applied to delayed stochastic linear-quadratic control problems. We prove the well-posedness of ABSDEs with quadratic growth and unbounded terminal values. To obtain the existence result, we first prove a priori estimate for the solutions and then use a limit argument. We also derive a comparison theorem using θ-technique, which gives uniqueness of the solution.