Outperformance Portfolio Optimization Via the Equivalence of Pure and Randomized Hypothesis Testing
34 Pages Posted: 27 Mar 2013 Last revised: 27 Jan 2015
Date Written: March 31, 2013
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.
Keywords: portfolio optimization, quantile hedging, stochastic benchmark, hypothesis testing, Neyman-Pearson lemma
JEL Classification: G10, G12, G13, D81
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