Forward-backward stochastic differential equations with Brownian motion and poisson process

Abstract

Existence and uniqueness results of the solution to fully coupled forward-backward stochastic differential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathematical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.