# Modélisation du risque de défaut en entreprise

Abstract : In the first part of this thesis, we study some optimal stopping time problems of the form :

$sup_{\tau\in \Delta, \tau\geq 0} \esp_v\left[g(V_{\tau})\right] \hbox{~or}~ sup_{\tau\in \Delta, \tau\geq 0} \esp_v\left[e^{-r\tau}\bar{g}(V_{\tau})\right],$
where $V$ is a stochastic process, $g$ and $\bar{g}$ two Borelian functions, $r>0$ and $\Delta$ is the set of
$\F^V_.$-stopping times ($\F^V$ being the filtration generated by the process $V$). These problems can be applied in Finance, Economy or Medicine.

In the first part of this thesis we show that sometimes the smallest optimal stopping time is a hitting time. That's why, in the second part we study the hitting time law of a Lévy jump process. Some applications to finance are given : we compute the intensity of this stopping time associated with some filtration $\F$. Two cases are presented : when the stopping time is a $\F$-stopping time and when it is not.
Keywords :
Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00257243
Contributor : Diana Dorobantu <>
Submitted on : Monday, February 18, 2008 - 6:16:14 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Thursday, May 20, 2010 - 10:43:43 PM

### Identifiers

• HAL Id : tel-00257243, version 1

### Citation

Diana Dorobantu. Modélisation du risque de défaut en entreprise. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2007. Français. ⟨tel-00257243⟩

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