Arrow Sufficient Conditions for Optimality of Fully Coupled Forward-Backward Stochastic Differential Equations with Applications to Finance

摘要

This paper is concerned with optimal control problems of fully coupled forward-backward stochastic differential equations on finite horizon and infinite horizon with partial information. Two sufficient conditions for optimality are established for the above problems. We demonstrate their applications by four illustrative examples in the framework of cash management, risk minimizing, and linear-quadratic optimal control problems. These examples are explicitly solved based on the sufficient conditions and the optimal filtering of forward-backward stochastic differential equations derived in this paper.