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

Finance and Stochastics - Tập 17 - Trang 839-870 - 2013
Tim Leung1, Qingshuo Song2, Jie Yang3
1Department of Industrial Engineering and Operations Research, Columbia University, New York, USA
2Department of Mathematics, City University of Hong Kong, Hong Kong, Hong Kong
3Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA

Tóm tắt

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.

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