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Adaptive Optimal Allocation in Stratified Sampling Methods

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Abstract

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%.

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References

  • Arouna B (2004) Adaptative Monte Carlo method, a variance reduction technique. Monte Carlo Methods Appl 10(1):1–24

    Article  MATH  MathSciNet  Google Scholar 

  • Cannamela C, Garnier J, Looss B (2008) Controlled stratification for quantile estimation. Ann Appl Stat. arXiv:0802.2426

  • Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, New York

    MATH  Google Scholar 

  • Glasserman P, Heidelberger P, Shahabuddin P (1999) Asymptotic optimal importance sampling and stratification for pricing path-dependent options. Math Financ 9(2):117–152

    Article  MATH  MathSciNet  Google Scholar 

  • Pedregal P (2004) Introduction to optimization. Springer, Berlin

    MATH  Google Scholar 

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Authors and Affiliations

  1. LJK, B.P. 53, 38041, Grenoble Cedex 9, France

    Pierre Étoré

  2. CERMICS, Projet MathFi ENPC-INRIA-UMLV, Université Paris-Est, 6 et 8 avenue Blaise Pascal, 77455, Marne La Vallée, Cedex 2, France

    Benjamin Jourdain

Authors
  1. Pierre Étoré
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  2. Benjamin Jourdain
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Corresponding author

Correspondence to Pierre Étoré.

Additional information

This research benefited from the support of the French National Research Agency (ANR) program ADAP’MC and the “Chair Risques Financiers”, Fondation du Risque.

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Étoré, P., Jourdain, B. Adaptive Optimal Allocation in Stratified Sampling Methods. Methodol Comput Appl Probab 12, 335–360 (2010). https://doi.org/10.1007/s11009-008-9108-0

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  • DOI: https://doi.org/10.1007/s11009-008-9108-0

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