Optimal stopping for partially observed piecewise-deterministic Markov processes

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• 作者：Adrien Brandejsky^a ; ^b ; ^d ; Benoî ; te de Saporta^c ; ^e ; ^a ; ^{saporta@math.u-bordeaux1.fr} ; Franç ; ois Dufour^b ; ^d ; ^a
• 关键词：60G40 ; 60J25 ; 93E20 ; 93E25 ; 93E10 ; 60K10
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：123
• 期：8
• 页码：3201-3238
• 全文大小：400 K

文摘

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an -optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence.