Variance reduction for discretised diffusions via regression

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Belomestny, Denis^1,2  Haefner, Stefan³  Nagapetyan, Tigran⁴  Urusov, Mikhail¹ 

[1] Univ Duisburg Essen, Essen, Germany

[2] RAS, IITP, Moscow, Russia

[3] PricewaterhouseCoopers GmbH, Frankfurt, Germany

[4] Univ Oxford, Oxford, England

关键词: Control variates;    Monte Carlo methods;    Regression methods;    Stochastic differential equations;    Weak schemes;   

DOI  :  10.1016/j.jmaa.2017.09.002

来源: Elsevier

【 摘 要 】

In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way the complexity order of the standard Monte Carlo algorithm (epsilon(-3) in the case of a first order scheme and epsilon(-2.5) in the case of a second order scheme) can be reduced down to epsilon(-2+delta) for any delta is an element of [0, 0.25) with epsilon being the precision to be achieved. These theoretical results are illustrated by several numerical examples. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free