Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

Maturity randomization for stochastic control problems

Auteur(s):

Code(s) de Classification MSC:

• 93E20 Optimal stochastic control
• 35C15 Integral representations of solutions of PDE
• 91B28 Finance, portfolios, investment

Résumé: 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.

Mots Clés: optimal stopping ; stochastic control ; uncertain volatility models

Date: 2004-09-08

Prépublication numéro: PMA-929