Necessary and Sufficient Conditions of Optimality for Optimal Control Problems of Forward and Backward Systems

Abstract

We consider a stochastic control problem, where the set of controls is convex and the system is governed by a nonlinear forward and backward stochastic differential equation. We derive necessary and sufficient optimality conditions in the form of a stochastic maximum principle. The results are stated in weak form. Moreover, under additional assumptions we obtain these results in global form. We apply our version of the stochastic maximum principle to the financial model of a cash flow valuation problem.