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Exponential Utility Maximization under Partial Information

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  • Michael Mania

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  • Marina Santacroce

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    Abstract

    We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem, which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE), which characterizes the optimal strategy. We examine two particular cases of diffusion market models, for which an explicit solution has been provided. Finally, we study the issue of suffciency of partial information.

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    File URL: http://www.icer.it/docs/wp2008/ICERwp24-08.pdf
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    Bibliographic Info

    Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 24-2008.

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    Length: 29 pages
    Date of creation: Jun 2008
    Date of revision:
    Handle: RePEc:icr:wpmath:24-2008

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    Related research

    Keywords: Backward stochastic differential equation; semimartingale market model; exponential utility maximization problem; partial information; suffcient filtration.;

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    References

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    1. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    2. Martin Schweizer, 1994. "Risk-Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342.
    3. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, vol. 13(1), pages 121-150, January.
    4. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    5. Michael Monoyios, 2004. "Performance of utility-based strategies for hedging basis risk," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 245-255.
    6. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, 05.
    7. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
    8. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
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