Optimal stopping via reinforced regression

TL;DR

This paper introduces a reinforced regression Monte Carlo method for numerically solving optimal stopping problems, enhancing standard regression techniques with adaptive basis functions based on previous estimates.

Contribution

It presents a novel reinforced regression approach that improves the accuracy of Monte Carlo algorithms for optimal stopping problems.

Findings

Demonstrates effectiveness through a financial mathematics example

Shows improved convergence over traditional regression methods

Provides a flexible framework for reinforcement in regression algorithms

Abstract

In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimated continuation values. The proposed methodology is illustrated by a numerical example from mathematical finance.