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Risks 2018, 6(1), 19; https://doi.org/10.3390/risks6010019

A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution

1
Actuarial Research Center, Department of Statistics, University of Haifa, Mount Carmel, 3498838 Haifa, Israel
2
Department of Economics and Business Management, Ariel University, Ariel 40700, Israel
*
Author to whom correspondence should be addressed.
Received: 4 January 2018 / Revised: 20 February 2018 / Accepted: 26 February 2018 / Published: 6 March 2018
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Abstract

In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ). View Full-Text
Keywords: global optimization; fractional programming; linear constraints; mean-variance model; optimal portfolio selection; Sharpe ratio global optimization; fractional programming; linear constraints; mean-variance model; optimal portfolio selection; Sharpe ratio
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Landsman, Z.; Makov, U.; Shushi, T. A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution. Risks 2018, 6, 19.

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