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Approximation par projections et simulations de Monte-Carlo des équations différentielles stochastiques rétrogrades.

Abstract : This thesis deals with the approximation of backward stochastic differential equations (BSDE) using regression-based Monte-Carlo methods. Applications are in the field of financial mathematics. In a first part, we propose a new algorithm for which we study the convergence with respect to its parameters. We next propose in a second part a modification of this algorithm which is better suited for applications and enables us to approximate with a given precision the solution of BSDE. We extend our results to the case of reflected BSDE in a third part. In the fourth part, we make numerical experiments on the previous algorithms. We finally conclude by giving ways of extending our work.
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https://pastel.archives-ouvertes.fr/pastel-00001396
Contributor : Ecole Polytechnique <>
Submitted on : Tuesday, July 27, 2010 - 2:42:46 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on: : Thursday, October 28, 2010 - 11:33:20 AM

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Jean-Philippe Lemor. Approximation par projections et simulations de Monte-Carlo des équations différentielles stochastiques rétrogrades.. Mathématiques [math]. Ecole Polytechnique X, 2005. Français. ⟨pastel-00001396⟩

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