Optimal stopping of McKean-Vlasov diffusions via regression on particle systems
It provides a theoretically grounded numerical method for optimal stopping in nonlinear Markov processes, which is a challenging problem in stochastic control.
The paper proposes a novel regression algorithm for solving optimal stopping problems for McKean-Vlasov diffusions using particle systems, proving its convergence and illustrating performance with a numerical example.
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.