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Rapport (Rapport De Recherche) Année : 2009

An anticipative stochastic calculus approach to pricing in markets driven by Lévy processes

Agnès Sulem
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Résumé

We use the Itô-Ventzell formula for forward integrals and Malliavin calculus to study the stochastic control problem associated to utility indifference pricing in a market driven by Lévy processes. This approach allows us to consider general possibly non-Markovian systems, general utility functions and possibly partial information based portfolios. In the special case of the exponential utility function $U_\alpha = - \exp(-\alpha x)\; ; $ $ \alpha >0$, we obtain asymptotics properties for vanishing $\alpha$. In the special case of full information based portfolios and no jumps, we obtain a recursive formula for the optimal portfolio in a non-Markovian setting.
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Dates et versions

inria-00439350 , version 1 (07-12-2009)

Identifiants

  • HAL Id : inria-00439350 , version 1

Citer

Bernt Oksendal, Agnès Sulem. An anticipative stochastic calculus approach to pricing in markets driven by Lévy processes. [Research Report] RR-7127, INRIA. 2009, pp.30. ⟨inria-00439350⟩
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