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Portfolio Optimization With Performance Ratios

Author

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  • 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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    Cited by:

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    2. Guohui Guan & Lin He & Zongxia Liang & Litian Zhang, 2024. "Optimal VPPI strategy under Omega ratio with stochastic benchmark," Papers 2403.13388, arXiv.org.

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