Adaptive optimal allocation in stratified sampling methods

Pierre Etoré (1, 2) , Benjamin Jourdain (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 MATHFI - Mathématiques financières

In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction. And our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm.

Mots clés: adaptive Monte Carlo methods; stratified sampling; mathematical finance

Domaines: Méthodologie [stat.ME]; Calcul [stat.CO]; Probabilités [math.PR]; Théorie [stat.TH]; Statistiques [math.ST]

Pierre Etoré, Benjamin Jourdain. Adaptive optimal allocation in stratified sampling methods. Methodology and Computing in Applied Probability, 2010, 12 (3), pp.335-360. ⟨10.1007/s11009-008-9108-0⟩. ⟨hal-00192540v2⟩