Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing

Tim Leung, Qingshuo Song () and Jie Yang ()

Finance and Stochastics, 2013, vol. 17, issue 4, 839-870

Abstract: We study the portfolio optimization 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 the 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Portfolio optimization; Quantile hedging; Neyman–Pearson lemma; Stochastic benchmark; Hypothesis testing; G10; G12; G13; D81; 60H30; 91G10 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-013-0213-8

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