An extension of the Clark–Ocone formula under benchmark measure for Lévy processes
| Autor: | Yeliz Yolcu Okur |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Statistics and Probability
Mathematical finance Mathematical analysis Conditional expectation Malliavin calculus Risk-neutral measure Malliavin derivative Mathematics::Probability Modeling and Simulation Local martingale Applied mathematics Martingale (probability theory) Martingale representation theorem Mathematics |
| Zdroj: | Stochastics. 84:251-272 |
| ISSN: | 1744-2516 1744-2508 |
| DOI: | 10.1080/17442508.2010.542817 |
| Popis: | The classical Clark–Ocone theorem states that any random variable can be represented as where denotes the conditional expectation, is a Brownian motion with canonical filtration and D denotes the Malliavin derivative in the direction of W. Since many applications in financial mathematics require representation of random variables with respect to risk neutral martingale measure, an equivalent martingale measure version of this theorem was stated by Karatzas and Ocone (Stoch. Stoch. Rep. 34 (1991), 187–220). In this paper, we extend these results to be valid for square integrable pure jump Levy processes with no drift and for square integrable Ito–Levy processes using Malliavin calculus and white noise analysis. This extension might be useful for some applications in finance. As an application of our result, we calculate explicitly the closest hedge strategy for the digital option whose pay-off, , is square integrable and the stock price is driven by a Levy process. |
| Databáze: | OpenAIRE |
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