Nadia Oudjane (EDF R&D et Université Paris Ouest)

We analyze the robustness properties of the Snell envelope backward evolution equation for the discrete time optimal stopping problem. In a first part, we consider a series of approximation schemes, including cut-off type approximations, Euler discretization schemes, interpolation models, quantization tree models and the Stochastic Mesh method of Broadie-Glasserman. In each situation, we provide non asymptotic convergence estimates. We deduce these estimates from a single and general robustness property of Snell envelope semigroups. In the second part, we propose a new approach based on a genealogical tree approximation model of the reference Markov process in terms of a neutral type genetic model. In contrast to Broadie-Glasserman Monte Carlo models, the computational cost of this new stochastic approximation is linear in the number of particles.