Mean-field backward stochastic differential equations on Markov chains

TL;DR

This paper studies mean-field backward stochastic differential equations linked to finite state Markov chains, establishing key theoretical results such as existence, uniqueness, and comparison theorems under Lipschitz conditions.

Contribution

It provides the first comprehensive analysis of mean-field BSDEs on Markov chains, including existence, uniqueness, and comparison theorems.

Findings

Proved existence and uniqueness of solutions.

Established a comparison theorem.

Extended BSDE theory to Markov chain context.

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.