Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems

TL;DR

This paper introduces a flexible forward improvement iteration algorithm for infinite horizon Markovian optimal stopping problems, enhancing efficiency by adjusting look-ahead windows and proving convergence.

Contribution

It extends existing algorithms by incorporating a flexible look-ahead window, reducing runtime and maintaining convergence in infinite horizon Markovian optimal stopping problems.

Findings

The algorithm converges under the proposed framework.

Flexible window parameter reduces computational runtime.

The method is applicable to problems with random discounting.

Abstract

In this paper, we propose an extension of the forward improvement iteration algorithm, originally introduced in Irle (2006) and recently reconsidered in Miclo and Villeneuve (2021). The main new ingredient is a flexible window parameter describing the look-ahead distance in the improvement step. We consider the framework of a Markovian optimal stopping problem in discrete time with random discounting and infinite time horizon. We prove convergence and show that the additional flexibility may significantly reduce the runtime.