Optimal stopping for partially observed piecewise-deterministic Markov processes

Abstract

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 actual $\epsilon$-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence.

References in corpus (4)

• On the long time behavior of the TCP window size process
• Numerical method for optimal stopping of piecewise deterministic Markov processes
• Finite Horizon Decision Timing with Partially Observable Poisson Processes
• Fluid limit theorems for stochastic hybrid systems with application to neuron models

Cited by in corpus (1)

• Optimal Control of Partially Observable Piecewise Deterministic Markov Processes