Risk-Sensitive Stopping Problems for Continuous-Time Markov Chains

TL;DR

This paper develops a framework for risk-sensitive stopping problems in continuous-time Markov chains, deriving optimality equations, proving existence of optimal stopping times, and analyzing the impact of risk sensitivity with practical examples.

Contribution

It introduces a general risk-sensitive criterion for stopping problems in continuous-time Markov chains and establishes the existence and characterization of optimal stopping times.

Findings

Optimal stopping times may occur between jumps due to risk sensitivity.

Derived optimality equations for the value functions.

Illustrated the approach with a house selling example.

Abstract

In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty equivalent of the stopping reward minus cost over the time horizon. We derive optimality equations for the value functions and prove the existence of optimal stopping times. The exponential utility is treated as a special case. In contrast to risk-neutral stopping problems it may be optimal to stop between jumps of the Markov chain. We briefly discuss the influence of the risk sensitivity on the optimal stopping time and consider a special house selling problem as an example.