Ergodic distribution dependent BSDE and application to long-time behavior of finite horizon distribution dependent BSDE

TL;DR

This paper establishes the existence and uniqueness of ergodic distribution dependent BSDEs under dissipativity conditions and applies these results to analyze long-time behavior in McKean--Vlasov stochastic control problems.

Contribution

It introduces a new framework for ergodic distribution dependent BSDEs and applies it to long-time analysis of finite horizon distribution dependent BSDEs and control problems.

Findings

Existence and uniqueness of ergodic distribution dependent BSDEs

Long-time behavior characterization of finite horizon distribution dependent BSDEs

Application to ergodic McKean--Vlasov stochastic control problems

Abstract

After proving existence and uniqueness of ergodic distribution dependent backward stochastic differential equations (BSDEs) under strong and weak dissipativity regimes for the underlying McKean--Vlasov SDE, we leverage this new framework to investigate the long-time behavior of distribution dependent BSDEs on a finite-time horizon. Finally, we apply our results to solve an ergodic McKean--Vlasov stochastic control problem and study the long-time behavior of the value function of a finite-horizon McKean--Vlasov stochastic control problem.