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Contrôle stochastique et applications à la couverture d'options en présence d'illiquidité: Aspects théoriques et numériques

Abstract : We study some applications of stochastic control to option hedge with illiquidity. In the first part, we focus on a superreplication problem in a stochastic volatility model. The specificity comes from the fact that the asset which is used to hedge volatility is illiquid, thus only a finite total amount of transactions can be operated during the hedging. The second part is about option hedging in presence of uncertain volatility, which dynamics are unspecified. We introduce a criterion to obtain non trivial prices, by allowing the agent to lose money for improbable volatility scenarios. At last, in the third part, we study an impulse control problem in which the actions take effect with delay. This can be applied for hedging options on hedge funds. Indeed, buying and selling orders on these funds are executed with delay. In each part, we characterize the value function of the problem as the unique viscosity solution of a partial differential equation. In the first and third parts, we also introduce, in a second chapter, numerical algorithms to solve those PDE with finite differences methods. Convergence of these algorithms is proved in a theoretical framework.
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https://tel.archives-ouvertes.fr/tel-00262019
Contributor : Benjamin Bruder <>
Submitted on : Monday, March 10, 2008 - 4:14:04 PM
Last modification on : Wednesday, December 9, 2020 - 3:09:35 PM
Long-term archiving on: : Friday, May 21, 2010 - 12:07:56 AM

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  • HAL Id : tel-00262019, version 1

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Benjamin Bruder. Contrôle stochastique et applications à la couverture d'options en présence d'illiquidité: Aspects théoriques et numériques. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00262019⟩

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