Optimal strategies for impulse control of piecewise deterministic Markov processes

TL;DR

This paper introduces a new explicit method for constructing epsilon-optimal impulse control strategies for piecewise deterministic Markov processes, avoiding complex auxiliary problems and relying only on the no-impulse cost.

Contribution

It presents a novel family of epsilon-optimal strategies that are explicitly constructed using a single-operator iteration, simplifying the control problem.

Findings

Explicit epsilon-optimal strategies without solving auxiliary problems

Strategies depend only on the no-impulse cost

Method applicable to general discounted impulse control of PDMPs

Abstract

This paper deals with the general discounted impulse control problem of a piecewise deterministic Markov process. We investigate a new family of epsilon-optimal strategies. The construction of such strategies is explicit and only necessitates the previous knowledge of the cost of the no-impulse strategy. In particular, it does not require the resolution of auxiliary optimal stopping problem or the computation of the value function at each point of the state space. This approach is based on the iteration of a single-jump-or-intervention operator associated to the piecewise deterministic Markov process.