@mastersthesis {69,
title = {M{\'e}thodes de quantification optimale avec applications {\`a} la finance},
year = {2008},
abstract = {This thesis is dovoted to optimal quantization with some applications to mathematical finance. Chap.1 reminds the bases of optimal quantization and numerical search of optimal quantizers. In chap.2 we study the asymptotics, in $L^s$, of the quantization error associated to a linear transform of an $L^r$ optimal sequence of quantizers. We show that such a transformation allows to make the transformed sequence $L^s$ rate optimal for every $s>0$, for a large family of probabilities. Chap.3 deals with the asymptotics of the maximal radius sequence associated to an $L^r$ optimal sequence of quantizers. We show that as soon as $\textrm{supp}(p)$ is unbounded, the maximal radius converge to infinity. We then give the rate of convergence for a large family of probabilities. Chap.4 is devoted to the pricing of lookback and barrier like options. We write these prices in a form which allows us to estimate them by Monte-Carlo, by an hybrid Monte-Carlo-quantization and by a pure quantization method. },
keywords = {barrier options, Lloyd algorithm, lookback options, maximal radius, quantization, rate-optimal},
author = {Abass Sagna}
}