A new approach to optimal stopping for Hunt processes

TL;DR

This paper introduces a novel verification theorem for optimal stopping problems involving Hunt processes, utilizing the Fukushima-Dynkin formula to verify value functions without viscosity solutions, applicable in any dimension.

Contribution

The paper presents a new verification theorem for Hunt processes that simplifies the verification of value functions without viscosity solutions, applicable in multiple dimensions.

Findings

Verification theorem applicable to any dimension

Applicable to reflected and absorbed diffusions

Simplifies the verification process

Abstract

In this paper we present a new verification theorem for optimal stopping problems for Hunt processes. The approach is based on the Fukushima-Dynkin formula, and its advantage is that it allows us to verify that a given function is the value function without using the viscosity solution argument. Our verification theorem works in any dimension. We illustrate our results with some examples of optimal stopping of reflected diffusions and absorbed diffusions.