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Habilitation à diriger des recherches

Contributions à la simulation et à l'analyse de discrétisation de processus, et applications.

Abstract : We present some contributions to the simulation of stochastic processes and to the analysis of discretization errors, with their applications in finance. Our works are divided into 4 items: 1. statistics for stochastic processes with discrete observations; 2. discrete time hedging in finance; 3. sensitivities of expectations; 4. analysis of discretization errors. The first chapter about statistics for stochastic processes can be read independently of the following ones. On the other hand, the three other chapters are coherent regarding the issues that are raised. However, we can identify some connections between the four parts: differentiation w.r.t. the boundary and improvment of the simulation of exit times; sensitivities of expectations and asymptotic statistics using Malliavin calculus; sensitivities of expectations and analysis of discretization errors... The proofs of our results are based in particular on the Malliavin calculus, the martingales theory, the partial differential equations and their connections with the stochastic differential equations.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00003841
Contributor : Hal System <>
Submitted on : Wednesday, November 26, 2003 - 2:17:05 PM
Last modification on : Thursday, December 10, 2020 - 10:52:44 AM
Long-term archiving on: : Friday, April 2, 2010 - 7:49:05 PM

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  • HAL Id : tel-00003841, version 1

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Emmanuel Gobet. Contributions à la simulation et à l'analyse de discrétisation de processus, et applications.. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2003. ⟨tel-00003841⟩

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