# Maturity randomization for stochastic control problems

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 CMAP - Centre de Mathématiques Appliquées 3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called {\it Canadization} procedure suggested by P. Carr in 2 for the fast computation of American put option prices. In addition to the original application of this technique to optimal stopping problems, we provide an application to another problem in finance, namely the super-replication problem under stochastic volatility, and we show that the approximating value functions can be computed explicitly.

keyword : optimal stopping stochastic control uncertain volatility models

Author: Bruno Bouchard - Nicole El Karoui - Nizar Touzi -

Source: https://hal.archives-ouvertes.fr/