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| HAL : hal-00617111, version 2 |
| arXiv : 1108.5264 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (26-08-2011) | v2 (13-02-2012) |
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| A Mean-Reverting SDE on Correlation matrices |
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| Abdelkoddousse Ahdida 1Aurélien Alfonsi 1 |
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| (26/08/2011) |
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| We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a useful connection with Wishart processes that makes understand how we get the full SDE. Then, we focus on the simulation of this diffusion and present discretization schemes that achieve a second-order weak convergence. Last, we explain how these correlation processes could be used to model the dependence between financial assets. |
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| 1 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| Domaine | : | Mathématiques/Probabilités Économie et finance quantitative/Finance quantitative |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00617111, version 2 | |
| http://hal-enpc.archives-ouvertes.fr/hal-00617111 | |
| oai:hal-enpc.archives-ouvertes.fr:hal-00617111 | |
| Contributeur : Alfonsi Aurélien | |
| Soumis le : Lundi 13 Février 2012, 11:03:48 | |
| Dernière modification le : Lundi 13 Février 2012, 13:39:31 | |
