Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1109.5316.
Date of creation: Sep 2011
Date of revision: Mar 2013
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Web page: http://arxiv.org/
Other versions of this item:
- Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, Springer, vol. 17(4), pages 839-870, October.
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-09 (All new papers)
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