Mean field control and finite dimensional approximation for regime-switching jump diffusions

TL;DR

This paper studies a mean field control problem involving jump-diffusions with regime switching, characterizing the value function via a master equation, and establishing convergence and propagation of chaos results.

Contribution

It introduces a novel analysis of mean field control with regime switching jump diffusions, including a viscosity solution characterization and explicit convergence rates.

Findings

Value function characterized as a viscosity solution of a master equation.

Proved convergence of finite agent control problem to mean field limit with explicit rate.

Established propagation of chaos for optimal agent trajectories under smoothness assumptions.

Abstract

We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability measures. Using this characterization, we prove that the value function, which is not regular, is the limit of a finite agent centralized optimal control problem as the number of agents go to infinity, with an explicit convergence rate. Assuming in addition that the value function is smooth, we establish a quantitative propagation of chaos result for the optimal trajectory of agent states.