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Abstract: In this article, we propose several quantization-based stratified samplingmethods to reduce the variance of a Monte Carlo simulation. Theoretical aspectsof stratification lead to a strong link between optimal quadratic quantizationand the variance reduction that can be achieved with stratified sampling. Wefirst put the emphasis on the consistency of quantization for partitioning thestate space in stratified sampling methods in both finite and infinitedimensional cases. We show that the proposed quantization-based strata designhas uniform efficiency among the class of Lipschitz continuous functionals.Then a stratified sampling algorithm based on product functional quantizationis proposed for path-dependent functionals of multi-factor diffusions. Themethod is also available for other Gaussian processes such as Brownian bridgeor Ornstein-Uhlenbeck processes. We derive in detail the case ofOrnstein-Uhlenbeck processes. We also study the balance between the algorithmiccomplexity of the simulation and the variance reduction factor



Autor: Sylvain Corlay LPMA, Gilles Pagès LPMA

Fuente: https://arxiv.org/



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