@mastersthesis {SellamiPhD,
title = {M{\'e}thodes de quantification optimale pour le filtrage et applications {\`a} la finance},
year = {2005},
school = {Universit{\'e} Paris Dauphine},
abstract = {We develop a grid based numerical approach to solve a filtering problem, using results on optimal quantization of random variables. We construct two filtering algorithms using zero order and first order approximation techniques. We suggest implementable versions of these algorithms and study the approximation error behavior by considering the stationnary property of optimal quantizers. The grid approach is then compared to the particle one based on Monte Carlo methods. The study is done over a set of different state models. In a second part, we have been interested in the advantadge given by quantization methods to preprocess offline the information. This permitted to develop a filtering algorithm based on observation (and signal) quantization. Here also the error convergence rate to zero as the quantizer size goes to infinity is studied. Finally, the quantization of the filter as a random variable is studied in order to solve a problem of pricing an American option in an unobserved stochastic volatility market. All results are illustrated by numerical experiments},
keywords = {American option, Filtering, Monte Carlo, offline preprocessing, optimal quantization, particle method, stationary quantizer, stochastic volatility},
attachments = {http://www.quantize.maths-fi.com/sites/default/files/PhD_AfefSELLAMI.pdf , http://www.quantize.maths-fi.com/sites/default/files/Introduction_Sellami.pdf},
author = {Afef Sellami}
}