Sufficient Stochastic Maximum Principle for Discounted Control Problem

TL;DR

This paper establishes a sufficient stochastic maximum principle for infinite horizon discounted control problems, applying it to population dynamics with stochastic logistic equations.

Contribution

It introduces a sufficient maximum principle under concavity assumptions, extending stochastic control theory to discounted infinite horizon problems with control in diffusion.

Findings

Sufficient maximum principle proven for discounted stochastic control.

Application to stochastic logistic population model demonstrated.

Control in diffusion term included in the analysis.

Abstract

In this article, the sufficient Pontryagin's maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function. Throughout the paper, it is assumed that the control domain U is a convex set and the control may enter the diffusion term of the state equation. The general results are applied to the controlled stochastic logistic equation of population dynamics.