The Annals of Applied Probability

Central limit theorem for the multilevel Monte Carlo Euler method

Mohamed Ben Alaya and Ahmed Kebaier

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 25, Number 1 (2015), 211-234.

Dates
First available in Project Euclid: 16 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1418740184

Digital Object Identifier
doi:10.1214/13-AAP993

Mathematical Reviews number (MathSciNet)
MR3297771

Zentralblatt MATH identifier
1320.60073

Subjects
Primary: 60F05: Central limit and other weak theorems 62F12: Asymptotic properties of estimators 65C05: Monte Carlo methods 60H35: Computational methods for stochastic equations [See also 65C30]

Keywords
Central limit theorem multilevel Monte Carlo methods Euler scheme finance

Citation

Ben Alaya, Mohamed; Kebaier, Ahmed. Central limit theorem for the multilevel Monte Carlo Euler method. Ann. Appl. Probab. 25 (2015), no. 1, 211--234. doi:10.1214/13-AAP993. https://projecteuclid.org/euclid.aoap/1418740184


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