Maximum principle for optimal control of forward-backward doubly stochastic differential equations with jumps

TL;DR

This paper establishes a maximum principle for optimal control of complex stochastic systems described by coupled forward-backward doubly stochastic differential equations with jumps, allowing coefficients to be random and control-dependent.

Contribution

It introduces a maximum principle for a new class of stochastic control problems involving coupled forward-backward systems with jumps and random coefficients.

Findings

Derived sufficient conditions for optimality.

Extended maximum principle to systems with jumps and random coefficients.

Applicable to complex stochastic control models.

Abstract

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.