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


  • Tim Leung
  • Qingshuo Song
  • Jie Yang


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,, revised Mar 2013.
  • Handle: RePEc:arx:papers:1109.5316

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    References listed on IDEAS

    1. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127,
    2. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    3. Jarrow, Robert A., 2010. "Understanding the risk of leveraged ETFs," Finance Research Letters, Elsevier, vol. 7(3), pages 135-139, September.
    4. Erhan Bayraktar & Yu-Jui Huang & Qingshuo Song, 2010. "Outperforming the market portfolio with a given probability," Papers 1006.3224,, revised Aug 2012.
    5. Marc Romano & Nizar Touzi, 1997. "Contingent Claims and Market Completeness in a Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 399-412.
    6. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    7. Birgit Rudloff, 2007. "Convex Hedging in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 437-452.
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    Cited by:

    1. repec:eee:stapro:v:137:y:2018:i:c:p:63-69 is not listed on IDEAS
    2. 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.
    3. Yao Tung Huang & Qingshuo Song & Harry Zheng, 2015. "Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk," Papers 1506.00082,, revised May 2016.

    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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