Neutral Backward Stochastic Functional Differential Equations and Their Application

TL;DR

This paper introduces neutral backward stochastic functional differential equations, establishes their mathematical properties, and applies these results to optimal control problems, including a maximum principle and explicit solutions.

Contribution

It defines a new class of backward stochastic equations, proves their existence, uniqueness, and comparison theorem, and applies these to control theory.

Findings

Existence and uniqueness of solutions established

Comparison theorem proved for the new equations

Explicit optimal control solutions derived

Abstract

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.