A stochastic maximum principle for partially observed stochastic control systems with delay

TL;DR

This paper develops a stochastic maximum principle for partially observed control systems with delay, using variational and filtering methods, and demonstrates its application through examples including an investment problem.

Contribution

It introduces a new maximum principle for delayed, partially observed stochastic control problems without requiring concavity assumptions.

Findings

The maximum principle is established for systems with delay.

Numerical simulations illustrate the delay's impact on optimal investment.

The approach combines variational, filtering, and discretization techniques.

Abstract

This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational method and a filtering technique. Also, we establish a sufficient condition without assumption of the concavity. Two examples shed light on the theoretical results are established in the paper. In particular, in the example of an optimal investment problem with delay, its numerical simulation shows the effect of delay via a discretization technique for forward-backward stochastic differential equations (FBSDEs) with delay and anticipate terms.