Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing
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
Cite
@article{arxiv.1109.5316,
title = {Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing},
author = {Tim Leung and Qingshuo Song and Jie Yang},
journal= {arXiv preprint arXiv:1109.5316},
year = {2015}
}
Comments
34 pages, 3 figures