Séminaire de la Chaire Finance et Développement Durable & de l’Initiative de Recherche Finance des Marchés d’Energies

Organisation : Delphine Lautier, Emmanuel Gobet, Clémence Alasseur

Lieu : Salle 01 – Institut Henri Poincaré, 11 rue Pierre et Marie Curie – Paris 5eme
Date : Vendredi 25 mars 2016

Heure : 14h00
Intervenants: Gang Liu (CMAP, Ecole Polytechnique)

Sujet: A non-intrusive stratified resampler for regression Monte Carlo: application to solving non-linear equations

Abstract: Our goal is to solve certain dynamic programming equations associated to a given Markov chain, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for the Markov chain is not known in full detail and only a root sample of such process is available. By a stratification of the space and a suitable choice of a probability measure, we design a new resampling scheme that allows to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows to compute the solution to the dynamic programming equation (possibly in large dimension) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish non-asymptotic error estimates. Our numerical experiments illustrate the good performance, even with only 20 or 40 root paths.

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