Adaptive Optimal Allocation in Stratified Sampling Methods

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• 作者：Pierre 脡tor茅 (1)
  Benjamin Jourdain (2)
  
• 关键词：Adaptive Monte Carlo methods ; Stratified sampling ; Finance ; 65C05 ; 91 ; 08 ; 60F05 ; 60G42
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2010
• 出版时间：September 2010
• 年：2010
• 卷：12
• 期：3
• 页码：335-360
• 全文大小：485KB
• 参考文献：1. Arouna B (2004) Adaptative Monte Carlo method, a variance reduction technique. Monte Carlo Methods Appl 10(1):1鈥?4 CrossRef
  2. Cannamela C, Garnier J, Looss B (2008) Controlled stratification for quantile estimation. Ann Appl Stat. arXiv:0802.2426
  3. Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, New York
  4. Glasserman P, Heidelberger P, Shahabuddin P (1999) Asymptotic optimal importance sampling and stratification for pricing path-dependent options. Math Financ 9(2):117鈥?52 CrossRef
  5. Pedregal P (2004) Introduction to optimization. Springer, Berlin
  
• 作者单位：Pierre 脡tor茅 (1)
  Benjamin Jourdain (2)
  
  1. LJK, B.P. 53, 38041, Grenoble Cedex 9, France
  2. CERMICS, Projet MathFi ENPC-INRIA-UMLV, Universit茅 Paris-Est, 6 et 8 avenue Blaise Pascal, 77455, Marne La Vall茅e, Cedex 2, France
  

文摘

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. For the pricing of arithmetic average Asian options in the Black and Scholes model, the variance is divided by a factor going from 1.1 to 50.4 (depending on the option type and the moneyness) in comparison with the standard allocation procedure, while the increase in computation time does not overcome 1%.