Asymptotic study of stochastic algorithms and computation of Parisian options prices.

Summary The first part of this thesis is devoted to the study of the randomly truncated stochastic algorithms of Chen and Zhu. The first study of this algorithm concerns its almost sure convergence. In the second chapter, we continue the study of this algorithm by focusing on its convergence speed. We also consider a moving average version of this algorithm. Finally we conclude with some applications to finance. The second part of this thesis focuses on the valuation of Parisian options based on the work of Chesney, Jeanblanc and Yor. The valuation method is based on obtaining closed formulas for the Laplace transforms of prices with respect to maturity. We establish these formulas for single and double barrier Parisian options. We then study a numerical inversion method of these transforms and establish its accuracy.