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Optimal investment under partial information

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  • Tomas Björk
  • Mark Davis
  • Camilla Landén

Abstract

We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory. Copyright Springer-Verlag 2010

Suggested Citation

  • Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:2:p:371-399
    DOI: 10.1007/s00186-010-0301-x
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    References listed on IDEAS

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    1. David Feldman, 1989. "The Term Structure of Interest Rates in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 44(3), pages 789-812, July.
    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. Giorgia Callegaro & Giovanni Masi & Wolfgang Runggaldier, 2006. "Portfolio Optimization in Discontinuous Markets under Incomplete Information," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 373-394, December.
    4. Dothan, Michael U & Feldman, David, 1986. "Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy," Journal of Finance, American Finance Association, vol. 41(2), pages 369-382, June.
    5. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    6. Honda, Toshiki, 2003. "Optimal portfolio choice for unobservable and regime-switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 45-78, October.
    7. Brennan, Michael J & Xia, Yihong, 2001. "Assessing Asset Pricing Anomalies," The Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 905-942.
    8. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    9. Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(4), pages 619-629, December.
    10. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    11. Jakša Cvitanić & Ali Lazrak & Lionel Martellini & Fernando Zapatero, 2006. "Dynamic Portfolio Choice with Parameter Uncertainty and the Economic Value of Analysts' Recommendations," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1113-1156.
    12. Nicole Bäuerle & Ulrich Rieder, 2007. "Portfolio Optimization With Jumps And Unobservable Intensity Process," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 205-224, April.
    13. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    14. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    15. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    16. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
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    More about this item

    Keywords

    Portfolio; Optimal control; Filtering; Partial information; Stochastic control; Partial observations; Investment; 49N30; 60H30; 93C41; 91G10; 91G80;
    All these keywords.

    JEL classification:

    • B26 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Financial Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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