Optimal stopping of McKean-Vlasov diffusions via regression on particle systems

TL;DR

This paper develops a new Monte Carlo regression algorithm for solving optimal stopping problems in McKean-Vlasov diffusions, with proven convergence and demonstrated effectiveness through numerical examples.

Contribution

It introduces a novel particle system-based regression method for nonlinear Markov processes and provides a convergence proof, advancing numerical solutions for such problems.

Findings

Algorithm converges under specified conditions

Numerical example demonstrates practical effectiveness

Provides a theoretical foundation for particle-based regression methods

Abstract

In this paper we study optimal stopping problems for nonlinear Markov processes driven by a McKean-Vlasov SDE and aim at solving them numerically by Monte Carlo. To this end we propose a novel regression algorithm based on the corresponding particle system and prove its convergence. The proof of convergence is based on perturbation analysis of a related linear regression problem. The performance of the proposed algorithms is illustrated by a numerical example.