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

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

2011-09-25

arxiv.org/abs/1109.5316v3

Economy

Quantitative Finance

Portfolio Management

28 pages, 3 figures

Scientific paper

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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