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inria-00439350, version 1

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

Bernt Oksendal () a1, Agnès Sulem () 2

N° RR-7127 (2009)

Abstract: 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.

• a –  University of Oslo
• 1:  Center of Mathematics for Applications [Oslo] (CMA)
• University of Oslo
• 2:  MATHFI (INRIA Rocquencourt)
• INRIA – Ecole des Ponts ParisTech – Université Paris-Est Créteil Val-de-Marne (UPEC)
• Domain : Quantitative Finance/Computational Finance
• Internal note : RR-7127

• inria-00439350, version 1
• oai:hal.inria.fr:inria-00439350
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• Submitted on: Monday, 7 December 2009 13:22:08
• Updated on: Tuesday, 19 January 2010 10:29:47