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 Ïμ-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence. © 2013 Elsevier B.V. All rights reserved.
Brandejsky, A., De Saporta, B., & Dufour, F. (2013). Optimal stopping for partially observed piecewise-deterministic Markov processes. Stochastic Processes and Their Applications, 123(8), 3201–3238. https://doi.org/10.1016/j.spa.2013.03.006