Solving optimal stopping problems via empirical dual optimization

TL;DR

This paper introduces a new simulation-based method for solving optimal stopping problems using dual representations, avoiding nested simulations, and demonstrates its effectiveness in option pricing scenarios.

Contribution

A novel, generic dual optimization algorithm for optimal stopping problems that converges and improves computational efficiency in option pricing.

Findings

Algorithm converges reliably

Effective in discrete and continuous time

Reduces computational complexity

Abstract

In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is proposed and studied. The algorithm involves the optimization of a genuinely penalized dual objective functional over a class of adapted martingales. We prove the convergence of the proposed algorithm and demonstrate its efficiency for optimal stopping problems arising in option pricing.