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A generalization of the mutual fund theorem


Author Info

  • Martin Kulldorff

    (Department of Statistics, Uppsala University, SE-75120 Uppsala, Sweden Manuscript)

  • Ajay Khanna

    (Stern School of Business Administration, New York University, New York, NY 10012 USA)

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    A generalization of the continuous time mutual fund theorem is given, with no assumptions made on the investors utility functions for consumption and final wealth, except that they are time-additive and non-decreasing. The extension is due to a new mathematical approach, using no more than simple properties of diffusion processes and standard linear algebra. The results are given for complete as well as certain incomplete markets. Moreover, optimal investment strategies that are known only for complete markets with a single risky asset, are automatically extended to complete and incomplete markets with multiple risky assets. An example is given.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 3 (1999)
    Issue (Month): 2 ()
    Pages: 167-185

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    Handle: RePEc:spr:finsto:v:3:y:1999:i:2:p:167-185

    Note: received: September 1997; final version received: April 1998
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    Related research

    Keywords: Portfolio selection; continuous time; separation theorem; reduction method; incomplete markets;


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    Cited by:
    1. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    2. Eckhard Platen, 2005. "Investments for the Short and Long Run," Research Paper Series 163, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Morten Christensen & Eckhard Platen, 2005. "Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps," Research Paper Series 170, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Erhan Bayraktar & Virginia R. Young, 2007. "Mutual Fund Theorems when Minimizing the Probability of Lifetime Ruin," Papers 0705.0053,, revised Mar 2008.
    5. Walter Schachermayer & Mihai Sîrbu & Erik Taflin, 2009. "In which financial markets do mutual fund theorems hold true?," Finance and Stochastics, Springer, vol. 13(1), pages 49-77, January.
    6. Framstad, N.C., 2011. "Portfolio separation properties of the skew-elliptical distributions, with generalizations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1862-1866.
    7. Eckhard Platen, 2005. "On the Role of the Growth Optimal Portfolio in Finance," Research Paper Series 144, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Dokuchaev, Nikolai & Yu Zhou, Xun, 2001. "Optimal investment strategies with bounded risks, general utilities, and goal achieving," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 289-309, April.
    9. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194,
    10. N. Dokuchaev & U. Haussmann, 2001. "Optimal portfolio selection and compression in an incomplete market," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 336-345.
    11. Platen, Eckhard, 2006. "Portfolio selection and asset pricing under a benchmark approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 23-29.


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