Dynamic programming for optimal stopping via pseudo-regression

TL;DR

This paper introduces a novel 'pseudo regression' approach for optimal stopping problems, replacing least-squares with Monte Carlo-based inner product approximation, leading to reduced computational complexity and validated by convergence analysis and numerical tests.

Contribution

It proposes a new pseudo regression method that improves efficiency of optimal stopping algorithms through Monte Carlo inner product approximation and detailed convergence analysis.

Findings

Lower computational cost for fixed error tolerance

Asymptotic convergence of the pseudo regression method

Validated effectiveness through numerical examples

Abstract

We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlying samples, we call the approach "pseudo regression". A detailed convergence analysis is provided and it is shown that the approach asymptotically leads to less computational cost for a pre-specified error tolerance, hence to lower complexity. The method is justified by numerical examples.