Optimal Stopping for Non-linear Expectations

TL;DR

This paper develops a theoretical framework for solving continuous-time optimal stopping problems where the decision-maker's evaluation of future rewards is based on non-linear risk measures, extending classical methods to more complex, risk-aware scenarios.

Contribution

It introduces a novel approach to optimal stopping under non-linear expectations, incorporating risk measures into the decision process.

Findings

Established a new theoretical foundation for non-linear optimal stopping.

Extended classical optimal stopping theory to risk-sensitive contexts.

Provided mathematical tools for practical implementation in risk-aware decision making.

Abstract

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.