A framework for adaptive Monte-Carlo procedures
AbstractAdaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptotic normality of the adaptive Monte Carlo estimator under local assumptions which are easily verifiable in practice. We present one way of approximating the optimal importance sampling parameter using a randomly truncated stochastic algorithm. Finally, we apply this technique to some examples of valuation of financial derivatives.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1001.3551.
Date of creation: Jan 2010
Date of revision: Jul 2010
Publication status: Published in Monte Carlo Methods and Applications 17, 1 (2011) 77-98
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-30 (All new papers)
- NEP-CMP-2010-01-30 (Computational Economics)
- NEP-ECM-2010-01-30 (Econometrics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152.
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