  In this paper we investigate a kind of optimal control problem of coupled
forward-backward stochastic system with jumps whose cost functional is defined
through a coupled forward-backward stochastic differential equation with
Brownian motion and Poisson random measure. For this end, we first study the
regularity of solutions for this kind of forward-backward stochastic
differential equations. We obtain that the value function is a deterministic
function and satisfies the dynamic programming principle for this kind of
optimal control problem. Moreover, we prove that the value functions is a
viscosity solutions of the associated Hamilton-Jacobi-Bellman equations with
integral-differential operators.

Probability;Optimization and Control