  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.
