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| HAL : inria-00484993, version 2 |
| arXiv : 1005.3608 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| Versions disponibles | v1 (20-05-2010) | v2 (26-10-2010) |
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| Clark-Ocone type formula for non-semimartingales with finite quadratic variation |
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| Cristina Di Girolami 1, 2Francesco Russo 2, 3, 4 |
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| (19/05/2010) |
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| We provide a suitable framework for the concept of finite quadratic variation for processes with values in a separable Banach space $B$ using the language of stochastic calculus via regularizations, introduced in the case $B= \R$ by the second author and P. Vallois. To a real continuous process $X$ we associate the Banach valued process $X(\cdot)$, called {\it window} process, which describes the evolution of $X$ taking into account a memory $\tau>0$. The natural state space for $X(\cdot)$ is the Banach space of continuous functions on $[-\tau,0]$. If $X$ is a real finite quadratic variation process, an appropriated Itô formula is presented, from which we derive a generalized Clark-Ocone formula for non-semimartingales having the same quadratic variation as Brownian motion. The representation is based on solutions of an infinite dimensional PDE. |
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| 1 : | Libera Universita Internazionale degli Studi Sociali Guido Carli di Roma (Luiss Guido Carli) |
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Libera Università Internazionale degli Studi Sociali |
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| 2 : | Unité de Mathématiques Appliquées (UMA) |
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ENSTA ParisTech |
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| 3 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 4 : | MATHFI (INRIA Rocquencourt) |
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INRIA – Ecole des Ponts ParisTech – Université Paris XII - Paris Est Créteil Val-de-Marne |
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| Unité de Mathématiques Appliquées, ENSTA ParisTech |
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| Domaine | : | Mathématiques/Probabilités |
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| Calculus via regularization – Infinite dimensional analysis – Clark-Ocone formula – Dirichlet processes – Itô formula – Quadratic variation – Hedging theory without semimartingales. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| inria-00484993, version 2 | |
| http://hal.inria.fr/inria-00484993 | |
| oai:hal.inria.fr:inria-00484993 | |
| Contributeur : Francesco Russo | |
| Soumis le : Mardi 26 Octobre 2010, 10:53:35 | |
| Dernière modification le : Mardi 26 Octobre 2010, 16:27:29 | |
