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Power utility maximization under partial information: Some convergence results

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  • Covello, D.
  • Santacroce, M.

Abstract

In this paper we consider the power utility maximization problem under partial information in a continuous semimartingale setting. Investors construct their strategies using the available information, which possibly may not even include the observation of the asset prices. Resorting to stochastic filtering, the problem is transformed into an equivalent one, which is formulated in terms of observable processes. The value process, related to the equivalent optimization problem, is then characterized as the unique bounded solution of a semimartingale backward stochastic differential equation (BSDE). This yields a unified characterization for the value process related to the power and exponential utility maximization problems, the latter arising as a particular case. The convergence of the corresponding optimal strategies is obtained by means of BSDEs. Finally, we study some particular cases where the value process admits an explicit expression.

Suggested Citation

  • Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:10:p:2016-2036
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    References listed on IDEAS

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    1. Huyên Pham, 2001. "Mean-Variance Hedging For Partially Observed Drift Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 263-284.
    2. 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.
    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. Martin Schweizer, 1994. "Risk‐Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 327-342, October.
    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. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    7. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    8. Kohlmann, Michael & Niethammer, Christina R., 2007. "On convergence to the exponential utility problem," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1813-1834, December.
    9. Christian Bender & Christina Niethammer, 2008. "On q-optimal martingale measures in exponential Lévy models," Finance and Stochastics, Springer, vol. 12(3), pages 381-410, July.
    10. 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.
    11. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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    Cited by:

    1. Oliver Janke, 2016. "Utility Maximization and Indifference Value under Risk and Information Constraints for a Market with a Change Point," Papers 1610.08644, arXiv.org.

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