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

Author

Listed:
  • 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 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.

Suggested Citation

  • Bernt Oksendal & Agnès Sulem, 2009. "An anticipative stochastic calculus approach to pricing in markets driven by Lévy processes," Working Papers inria-00439350, HAL.
    • Handle: RePEc:hal:wpaper:inria-00439350
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00439350
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    References listed on IDEAS

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    1. Fred Benth & Thilo Meyer-Brandis, 2005. "The density process of the minimal entropy martingale measure in a stochastic volatility model with jumps," Finance and Stochastics, Springer, vol. 9(4), pages 563-575, October.
    2. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    3. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    4. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
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