Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

This paper focuses on the study of an original combination of the Euler Multilevel Monte Carlo introduced by Giles  and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the importance sampling method, we rely on Robbins-Monro type stochastic algorithms. On the one hand, we extend our previous work to the Multilevel Monte Carlo setting. On the other hand, we improve  by providing a new adaptive algorithm avoiding the discretization of any additional process. We firstly prove the almost sure convergence of this stochastic algorithm towards the optimal parameter. Then, we prove a central limit theorem of type Lindeberg-Feller for the new adaptive Euler Multilevel Monte Carlo algorithm.
Finally, we illustrate the efficiency of our method through applications in option pricing.