A global stochastic maximum principle for delayed forward-backward stochastic control systems

TL;DR

This paper develops a global stochastic maximum principle for delayed forward-backward stochastic control systems with non-convex control domains, introducing new auxiliary equations and a novel derivation method.

Contribution

It presents a new method using auxiliary equations to derive the maximum principle for complex delayed stochastic control systems with non-convex controls.

Findings

Established a global stochastic maximum principle for the system.

Introduced first-order and second-order auxiliary equations.

Provided a novel approach to deriving adjoint and variational equations.

Abstract

In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is obtained by using a new method. More precisely, this method introduces first-order and second-order auxiliary equations and offers a novel approach to deriving the adjoint equations as well as the variational equation for $y^\e - y^*$.