Section: New Results

Numerical approximation for optimal stopping of MDP under partial observation

Participants : Benoîte de Saporta, François Dufour, Christophe Nivot.

We consider the optimal stopping problem for a continuous finite-dimensional state space Markov chain under partial observation. Our aim is to build a numerical approximation of the value function. To do so, we first translate the problem into the Partially Observed Markov Decision Process (POMDP) framework. Then, we define the equivalent fully observed Markov Decision Process (MDP) on an infinite dimensional state space. Finally, we proposed a discretization scheme based on the discretization of an underlying measure to obtain a finite dimensional problem and a discretization of the resulting state space to obtain a fully discrete model that is numerically tractable. We prove the convergence of the approximation procedure. This work is still in progress and was presented at the workshop [31]