# On some expectation and derivative operators related to integral representations of random variables with respect to a PII process

6 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
Abstract : 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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Type de document :
Pré-publication, Document de travail
29 pages. 2012
Domaine :

https://hal-ensta.archives-ouvertes.fr/hal-00665852
Contributeur : Francesco Russo <>
Soumis le : jeudi 2 février 2012 - 20:30:17
Dernière modification le : jeudi 5 janvier 2017 - 01:53:18
Document(s) archivé(s) le : jeudi 3 mai 2012 - 03:10:46

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### Identifiants

• HAL Id : hal-00665852, version 1
• ARXIV : 1202.0619

### Citation

Stéphane Goutte, Nadia Oudjane, Francesco Russo. On some expectation and derivative operators related to integral representations of random variables with respect to a PII process. 29 pages. 2012. <hal-00665852>

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