Partially Observed Optimal Stopping Problem
Benoîte de Saporta, François Dufour, Huilong Zhang · 2015
This chapter investigates the optimal stopping problem under partial observation for piecewise-deterministic Markov processes (PDMPs), both from theoretical and numerical points of view. It first defines the optimal stopping problem, especially the observation process and presents the assumptions. The recursive formulation of the filter process is then derived. The chapter also derives a property of the conditional expectation of the PDMP with respect to the filtration generated by the state and observation processes. Next, it reduces the partially observed problem for the PDMP (Xt)t=0 to a completely observed one involving the Markov process for which the authors provide the dynamic programming equation and construct a family of ϵ-optimal stopping times. Then, the numerical methods used to compute the approximation of the value function and the ϵ-optimal stopping time are presented where the authors also prove the convergence of the algorithms used by them.