A Stochastic Maximum Principle for Markov chains of mean-field type

TL;DR

This paper develops a stochastic maximum principle for optimal control problems involving mean-field type Markov chains, providing necessary and sufficient conditions for optimality in systems modeled by pure jump processes.

Contribution

It introduces a new SMP framework for mean-field Markov chains driven by pure jump processes, extending control theory to this class of stochastic systems.

Findings

Derived necessary and sufficient optimality conditions

Applied the framework to control problems and practical examples

Extended control theory to mean-field Markov jump processes

Abstract

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications.