On the Finite Horizon Optimal Switching Problem with Random Lag

TL;DR

This paper studies an optimal switching problem incorporating random delays and component failures, modeling mode transitions with a Markov process and using probabilistic methods to prove the existence of an optimal control.

Contribution

It introduces a novel framework combining random lag and failure modes in optimal switching problems, with a proof of optimal control existence using Snell envelopes.

Findings

Existence of an optimal control is established.

The model accounts for random delays and component failures.

Probabilistic techniques are effectively applied to complex switching problems.

Abstract

We consider an optimal switching problem with random lag and possibility of component failure. The random lag is modeled by letting the operation mode follow a regime switching Markov-model with transition intensities that depend on the switching mode. The possibility of failures is modeled by having absorbing components. We show existence of an optimal control for the problem by applying a probabilistic technique based on the concept of Snell envelopes.