Optimal stopping under model uncertainty: randomized stopping times approach

TL;DR

This paper introduces a new approach to optimal stopping problems under model uncertainty using randomized stopping times, extending dual representations and providing Monte Carlo algorithms for risk measures like Average Value at Risk.

Contribution

It generalizes the dual representation of optimal stopping to non-time-consistent risk measures and develops Monte Carlo methods for practical implementation.

Findings

Extended dual representation for non-time-consistent risk measures

Developed Monte Carlo algorithms for optimal stopping under Average Value at Risk

Demonstrated effectiveness of methods through numerical experiments

Abstract

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we generalise the additive dual representation of Rogers (2002) to the case of optimal stopping under uncertainty. Finally, we develop several Monte Carlo algorithms and illustrate their power for optimal stopping under Average Value at Risk.