Numerical method for impulse control of Piecewise Deterministic Markov Processes

TL;DR

This paper introduces a numerical quantization-based method to compute the value function in impulse control problems for piecewise deterministic Markov processes, providing convergence guarantees and rates.

Contribution

It develops a new quantization approach for solving impulse control problems in PDMPs, with proven convergence and explicit rates.

Findings

The method converges to the true value function.

Convergence rate of the algorithm is established.

Numerical example demonstrates practical effectiveness.

Abstract

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying Markov chain defined by the post jump location and inter-arrival time. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. The paper is illustrated by a numerical example.