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arXiv · 1109.5316

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

Tim Leung·Qingshuo Song·Jie Yang
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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.

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Tim Leung, Qingshuo Song, Jie Yang. 2013-03-31. Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing. https://doi.org/10.1007/s00780-013-0213-8

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