A NOTE ON SEMIVARIANCE

Hanqing Jin, Harry Markowitz and Xun Yu Zhou

Mathematical Finance, 2006, vol. 16, issue 1, 53-61

Abstract: In a recent paper (Jin, Yan, and Zhou 2005), it is proved that efficient strategies of the continuous‐time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below‐target semivariance model the attainability is established under the arbitrage‐free condition. Finally, we extend the results to problems with general downside risk measures.

Date: 2006
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