CENTRAL LIMIT THEOREM FOR THE MULTILEVEL MONTE CARLO EULER METHOD

被引：22

作者：

Ben Alaya, Mohamed ^{[1
]}

Kebaier, Armed ^{[1
]}

机构：

[1] Univ Paris 13, Sorbonne Paris Cite, CNRS UMR 7539, LAGA, F-93430 Villetaneuse, France

来源：

ANNALS OF APPLIED PROBABILITY | 2015年 / 25卷 / 01期

关键词：

Central limit theorem; multilevel Monte Carlo methods; Euler scheme; finance; COMPLEXITY;

D O I：

10.1214/13-AAP993

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the limiting variance in the central limit theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.

引用

页码：211 / 234

页数：24

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