On randomized stopping

TL;DR

This paper presents a general theorem on randomized stopping, applying it to simplify optimal stopping problems for controlled diffusions with unbounded coefficients, inspired by Krylov's work on Bellman equations.

Contribution

It introduces a broad result on randomized stopping and applies it to transform complex optimal stopping problems into more manageable control problems.

Findings

General result on randomized stopping proved

Application to controlled diffusions with unbounded coefficients

Reduction of optimal stopping to optimal control

Abstract

A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated by recent results of Krylov on numerical solutions to the Bellman equation.