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A generalization of the mutual fund theorem


  • 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)


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.

Suggested Citation

  • Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
  • 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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    Cited by:

    1. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194,
    2. 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.
    3. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    4. Bayraktar, Erhan & Young, Virginia R., 2008. "Mutual fund theorems when minimizing the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(2), pages 69-78, June.
    5. 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, March.
    6. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    7. 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.
    8. Morten Mosegaard Christensen & Eckhard Platen, 2007. "Sharpe Ratio Maximization And Expected Utility When Asset Prices Have Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(08), pages 1339-1364.
    9. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    10. Framstad, N.C., 2011. "Portfolio separation properties of the skew-elliptical distributions, with generalizations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1862-1866.
    11. Eckhard Platen, 2005. "Investments for the Short and Long Run," Research Paper Series 163, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. 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.
    13. Minjie Yu & Qiang Zhang & Dennis Yang, 2008. "Bankruptcy in long-term investments," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 777-794.


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