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Theses

Convergence de filtrations ; application à la discrétisation de processus et à la stabilité de temps d'arrêt.

Abstract : This thesis deals with properties of stability of stopping problems when we don't have all the information on the model. The natural filtration of a process represent the information carried by the process along the time. Then, the properties of the sequences of natural filtrations associated to the processes are very important in this work. A first part of this study is about the stability of the notions of value in optimal stopping problem and of optimal stopping time. The first notion is the maximum value of the expectation of a function that depends on a process and on a stopping time, value taken on the set of stopping times for the natural filtration of the process. An optimal stopping time is a stopping time which realises the maximum. The second part is about the stability of the solutions of a backward stochastic differential equation with an almost surely finite terminal time when the Brownian motion that drives the equation is approximated either by a sequence of random walks, either by a sequence of martingales.
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https://tel.archives-ouvertes.fr/tel-00011277
Contributor : Sandrine Toldo <>
Submitted on : Monday, January 2, 2006 - 2:48:02 PM
Last modification on : Thursday, January 7, 2021 - 4:12:46 PM
Long-term archiving on: : Saturday, April 3, 2010 - 7:58:02 PM

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  • HAL Id : tel-00011277, version 1

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Sandrine Toldo. Convergence de filtrations ; application à la discrétisation de processus et à la stabilité de temps d'arrêt.. Mathématiques [math]. Université Rennes 1, 2005. Français. ⟨tel-00011277⟩

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