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| HAL : hal-00665852, version 1 |
| arXiv : 1202.0619 |
| Fiche détaillée |  Récupérer au format |
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| On some expectation and derivative operators related to integral representations of random variables with respect to a PII process |
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| Stéphane Goutte 1Nadia Oudjane 2, 3 |
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| (02/02/2012) |
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| Given a process with independent increments $X$ (not necessarily a martingale) and a large class of square integrable r.v. $H=f(X_T)$, $f$ being the Fourier transform of a finite measure $\mu$, we provide explicit Kunita-Watanabe and Föllmer-Schweizer decompositions. The representation is expressed by means of two significant maps: the expectation and derivative operators related to the characteristics of $X$. We also provide an explicit expression for the variance optimal error when hedging the claim $H$ with underlying process $X$. Those questions are motivated by finding the solution of the celebrated problem of global and local quadratic risk minimization in mathematical finance. |
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| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| 2 : | EDF R&D |
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EDF |
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| 3 : | Laboratoire Analyse, Géométrie et Application (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| 4 : | École Nationale Supérieure de Techniques Avancées (ENSTA ParisTech) |
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ENSTA ParisTech |
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| 5 : | Unité de Mathématiques Appliquées (UMA) |
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ENSTA ParisTech |
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| 6 : | MATHRISK (INRIA Paris-Rocquencourt) |
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INRIA – Ecole des Ponts ParisTech – Université Paris-Est Marne-la-Vallée (UPEMLV) |
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| Domaine | : | Mathématiques/Probabilités |
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| Föllmer-Schweizer decomposition – Kunita-Watanabe decomposition – Lévy processes – Characteristic functions – Processes with independent increments – global and local quadratic risk minimization – expectation and derivative operators. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00665852, version 1 | |
| http://hal-ensta.archives-ouvertes.fr/hal-00665852 | |
| oai:hal-ensta.archives-ouvertes.fr:hal-00665852 | |
| Contributeur : Francesco Russo | |
| Soumis le : Jeudi 2 Février 2012, 20:30:17 | |
| Dernière modification le : Mardi 27 Mars 2012, 13:26:18 | |
