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

2 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
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.
Document type :
Reports (Research report)

Cited literature [17 references]

https://hal.inria.fr/inria-00439350
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Submitted on : Monday, December 7, 2009 - 1:22:08 PM
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RR-7127.pdf
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• HAL Id : inria-00439350, version 1

### Citation

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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