A framework for adaptive Monte-Carlo procedures

Bernard Lapeyre and J\'er\^ome Lelong
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Bernard Lapeyre: CERMICS
J\'er\^ome Lelong: LJK

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Abstract: Adaptive 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.

Date: 2010-01, Revised 2010-07
New Economics Papers: this item is included in nep-cmp and nep-ecm
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Published in Monte Carlo Methods and Applications 17, 1 (2011) 77-98

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1001.3551

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