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Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing

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  • Tim Leung
  • Qingshuo Song
  • Jie Yang

Abstract

We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be formulated as a composite pure hypothesis testing problem. We analyze the connection between this pure testing problem and its randomized counterpart, and from latter we derive a dual representation for the maximal outperformance probability. Moreover, in a complete market setting, we provide a closed-form solution to the problem of beating a leveraged exchange traded fund. For a general benchmark under an incomplete stochastic factor model, we provide the Hamilton-Jacobi-Bellman PDE characterization for the maximal outperformance probability.

Suggested Citation

  • Tim Leung & Qingshuo Song & Jie Yang, 2011. "Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing," Papers 1109.5316, arXiv.org, revised Mar 2013.
    • Handle: RePEc:arx:papers:1109.5316
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    References listed on IDEAS

    as
    1. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    2. Jarrow, Robert A., 2010. "Understanding the risk of leveraged ETFs," Finance Research Letters, Elsevier, vol. 7(3), pages 135-139, September.
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    7. Erhan Bayraktar & Yu-Jui Huang & Qingshuo Song, 2010. "Outperforming the market portfolio with a given probability," Papers 1006.3224, arXiv.org, revised Aug 2012.
    8. Krutchenko, R. & Melnikov, A., 2000. "Quantile hedging for a jump-diffusion financial market model," SFB 373 Discussion Papers 2000,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Ji, Shaolin & Shi, Xiaomin, 2018. "Reaching goals under ambiguity: Continuous-time optimal portfolio selection," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 63-69.
    2. Yao Tung Huang & Qingshuo Song & Harry Zheng, 2015. "Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk," Papers 1506.00082, arXiv.org, revised May 2016.
    3. Erhan Bayraktar & Gu Wang, 2018. "Quantile Hedging in a semi-static market with model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 197-227, April.
    4. Jan Obloj & Johannes Wiesel, 2018. "A unified Framework for Robust Modelling of Financial Markets in discrete time," Papers 1808.06430, arXiv.org, revised Dec 2019.

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    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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