Maximum principle for optimal control of forward-backward doubly stochastic differential equations with jumps

AbdulRahman Al-Hussein, Boulakhras Gherbal

Published 2013-01-09, updated 2013-08-27Version 4

In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with Poisson jumps. Moreover, all the coefficients appearing in this system are allowed to be random and depend on the control variable. We derive, in particular, sufficient conditions for optimality for this stochastic optimal control problem.