A Maximum Principle for Mean-Field SDEs with time change

TL;DR

This paper develops a maximum principle for mean-field stochastic differential equations with time change, addressing existence, uniqueness, and control problems in models driven by time-changed Brownian and Poisson measures.

Contribution

It introduces a maximum principle for mean-field SDEs with time change and analyzes solutions to associated backward SDEs, extending stochastic control theory.

Findings

Established existence and uniqueness of solutions to mean-field SDEs with time change.

Derived necessary and sufficient maximum principles for control problems.

Provided an economic example illustrating the application of the theory.

Abstract

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field stochastic differential equation. We consider a mean-field stochastic control problem for mean-field controlled dynamics and we present a necessary and a sufficient maximum principle. For this we study existence and uniqueness of solutions to mean-field backward stochastic differential equations in the context of time change. An example of a centralised control in an economy with specialised sectors is provided.