On the Continuity of Stochastic Exit Time Control Problems

TL;DR

This paper establishes a less restrictive condition ensuring the continuity of value functions in stochastic exit time control problems, improving theoretical understanding in stochastic control theory.

Contribution

It introduces a weaker sufficient condition than previous results for the continuity of value functions in stochastic exit time control problems.

Findings

Provided a new weaker condition for continuity

Extended theoretical framework of stochastic control

Improved understanding of value function properties

Abstract

We determine a weaker sufficient condition than that of Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions of stochastic exit time control problems.