Arouna, Bouhari (2004) Monte Carlo Methods and stochastic approximations. PhD thesis, ENPC.
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.
| Item Type: | PhD Thesis (PhD) |
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| Thesis Supervisor: | Lapeyre, Bernard |
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| Date: | December 2004 |
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| Board of examiners: | Pages, Gilles and Talay, Denis and Lacroix, Jean and Lamberton, Damien and Tyc, Stéphane and Lapeyre, Bernard |
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| Collection (Fonds): | ENPC |
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| Institution: | ENPC |
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| Subjects: | 1. Mathematics and Applications |
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| Uncontrolled Keywords: | Monte Carlo methods, Importance Sampling, Robbins-Monro Algorithms, Martingales, Chen Projection method, Méthode de Monte Carlo, Réduction de variance, Algorithmes Stochastiques, Projection fixe, Projection aléatoire "à la Chen", Martingales, Entropie relative |
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