Risk sensitive optimal stopping

TL;DR

This paper investigates risk-sensitive optimal stopping problems in both discrete and continuous time, establishing continuity of the value function, deriving optimal policies, and connecting discrete and continuous frameworks through approximation and convergence analysis.

Contribution

It provides new results on the continuity of the value function and formulas for optimal policies in risk-sensitive stopping, linking discrete and continuous models.

Findings

Proved continuity of the optimal stopping value function.

Derived explicit formulas for optimal stopping policies.

Established uniform convergence between discrete and continuous models.

Abstract

In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula for the optimal stopping policy. Next, we show how to link continuous time framework with its discrete time analogue. By considering suitable approximations, we obtain uniform convergence of the corresponding value functions.