A maximum principle for infinite horizon delay equations

TL;DR

This paper develops a maximum principle framework for optimal control problems involving stochastic delay equations over an infinite horizon, providing necessary and sufficient conditions and demonstrating an economic application.

Contribution

It introduces a novel maximum principle for stochastic delay equations on infinite horizons, including both necessary and sufficient conditions, with practical economic application.

Findings

Established first and second sufficient stochastic maximum principles.

Derived necessary conditions for optimal control.

Applied the theory to an economic consumption problem.

Abstract

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results by an application to the optimal consumption rate from an economic quantity.