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Portfolio Optimization With Performance Ratios

Author

Listed:
  • HONGCAN LIN

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada)

  • DAVID SAUNDERS

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada)

  • CHENGGUO WENG

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada)

Abstract

We consider the portfolio selection problem of maximizing a performance measure in a continuous-time diffusion model. The performance measure is the ratio of the overperformance to the underperformance of a portfolio relative to a benchmark. Following a strategy from fractional programming, we analyze the problem by solving a family of related problems, where the objective functions are the numerator of the original problem minus the denominator multiplied by a penalty parameter. These auxiliary problems can be solved using the martingale method for stochastic control. The existence of solution is discussed in a general setting and explicit solutions are derived when both the reward and the penalty functions are power functions.

Suggested Citation

  • Hongcan Lin & David Saunders & Chengguo Weng, 2019. "Portfolio Optimization With Performance Ratios," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-38, August.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:05:n:s0219024919500225
    DOI: 10.1142/S0219024919500225
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    References listed on IDEAS

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    1. Lin, Hongcan & Saunders, David & Weng, Chengguo, 2017. "Optimal investment strategies for participating contracts," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 137-155.
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    7. Bernard, Carole & Vanduffel, Steven & Ye, Jiang, 2019. "Optimal strategies under Omega ratio," European Journal of Operational Research, Elsevier, vol. 275(2), pages 755-767.
    8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

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