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Contributions à l'étude des marchés discontinus par le calcul de Malliavin

Abstract : We consider markets driven by normal martingales which have the chaotic representation property, e.g.: martingales satisfying a deterministic structure equation, Azéma martingales. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the Delta-hedging method, depending on which is most appropriate. Using the Malliavin calculus on Poisson space we compute Greeks for Asian options in a market driven by a Poisson process. We also consider a stochastic volatility model with jumps where the underlying asset price is driven by process sum of a 2-dimensional Brownian motion and Poisson process. The market is incomplete and there exists an infinity of equivalent martingale measures. We minimize the entropy to choose such a measure, under which we determine the strategy minimizing the variance.
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Contributor : Youssef El-Khatib <>
Submitted on : Saturday, January 17, 2004 - 10:26:53 AM
Last modification on : Friday, April 9, 2021 - 3:46:09 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 4:05:07 PM


  • HAL Id : tel-00003912, version 2



Youssef El-Khatib. Contributions à l'étude des marchés discontinus par le calcul de Malliavin. Mathématiques [math]. Université de la Rochelle, 2003. Français. ⟨tel-00003912v2⟩



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