NUMERICAL METHOD FOR OPTIMAL STOPPING OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

• 成果类型: Article
• 署名作者: de Saporta, Benoite; Dufour, Francois; Gonzalez, Karen
• 署名单位: Universite de Bordeaux
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP667
• 发表日期: 2010
• 页码: 1607-1637
• 关键词: quantization; STABILITY

摘要

We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location-inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable epsilon-optimal stopping time. The paper is illustrated by a numerical example.