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Monte Carlo Methods and stochastic approximations

Bouhari Arouna
Abstract : The objectiv of this work is to present new competitive variance reduction techniques for Monte Carlo simulations. The methods use importance sampling scheme. By an elementary change of variable, we introduce a drift term into the computation of an expectation via Monte Carlo simluations. Subsequently, the basic idea is to use a truncated version of the Robbins-Monro alogorithms to find the optimal drift that reduces the variance. First, we develop a seqential application of the method, in which the optimal drift is estimated separatly and is plugged in the Monte Carlo simulation. In the second part of our work we develop an adaptative version of the method, where the change of drift is selected dynamically through the Monte Carlo simulation. The last part of the work follows a similar idea but its main contribution is the introduction of a new minimisation criterion: the Kullback-Leibler entropy (or relative entropy) between two probability measures. We develop two applications of the procedure for variance reduction in Monte Carlo computation in finance an in reliability.
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Contributor : Ecole Des Ponts Paristech <>
Submitted on : Friday, June 3, 2005 - 8:00:00 AM
Last modification on : Friday, June 3, 2005 - 8:00:00 AM
Long-term archiving on: : Thursday, September 30, 2010 - 6:45:25 PM


  • HAL Id : pastel-00001269, version 1



Bouhari Arouna. Monte Carlo Methods and stochastic approximations. Mathematics [math]. Ecole des Ponts ParisTech, 2004. English. ⟨pastel-00001269⟩



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