Section: New Results

Optimal stopping under partial observation

Participants : Adrien Brandejsky, Benoîte de Saporta, François Dufour.

In continuation of our work on optimal stopping for Piecewise deterministic Markov processes (PDMP's) [8] , we have started investigating the optimal stopping problem when the process is only partially observed. We supposed that the jump times of the process are observed, but the post jump locations are observed through a noise.

The first step is to rewrite the optimal stopping problem for the partially observed PDMP as a totally observed stopping problem for a new Markov chain, obtained by filtering the observation process. Then, one has to study precisely this filter, which is non standard due to the possible jumps of the process. The next step is to derive the dynamic programming equation adapted to our framework. Finally, we propose a numerical method based on quantization to approximate the value function and $ϵ$-stopping times. Track is also kept of the error bounds all through our numerical procedure.

This work is still in progress and should be submitted to an international peer-reviewed journal shortly.