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

Bernt Oksendal () and Agnès Sulem ()
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Bernt Oksendal: CMA - Center of Mathematics for Applications [Oslo] - Department of Mathematics [Oslo] - Faculty of Mathematics and Natural Sciences [Oslo] - UiO - University of Oslo
Agnès Sulem: MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12

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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.

Date: 2009
Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00439350v1
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Published in [Research Report] RR-7127, INRIA. 2009, pp.30

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