On differentiability of reward functionals corresponding to Markovian randomized stopping times

TL;DR

This paper investigates the differentiability and continuity of reward functionals linked to Markovian randomized stopping times, emphasizing the importance of differentiability for deriving analytic expressions of the reward function.

Contribution

It provides new insights into the differentiability properties of reward functionals associated with Markovian randomized stopping times.

Findings

Analyzes conditions for differentiability of reward functionals

Establishes continuity properties of reward functionals

Highlights the role of differentiability in analytic derivations

Abstract

We conduct an investigation of the differentiability and continuity of reward functionals associated to Markovian randomized stopping times. Our focus is mostly on the differentiability, which is a crucial ingredient for a common approach to derive analytic expressions for the reward function.