Infinite horizon optimal control of forward-backward stochastic differential equations with delay

TL;DR

This paper develops maximum principles for infinite horizon optimal control of forward-backward stochastic differential equations with delay, under partial information, and demonstrates their application to recursive utility maximization in delayed cash flows.

Contribution

It introduces new maximum principles for infinite horizon control of delayed forward-backward stochastic systems under partial information.

Findings

Derived necessary and sufficient maximum principles.

Applied results to optimal consumption with recursive utility.

Extended control theory to systems with delay and partial information.

Abstract

We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.