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Mathematical Problems in Engineering
Volume 2017, Article ID 6279859, 17 pages
Research Article

A Parametric Sharpe Ratio Optimization Approach for Fuzzy Portfolio Selection Problem

Risk Management & Financial Engineering Laboratory, College of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, China

Correspondence should be addressed to Ya-Nan Li; moc.anis@200170ilnanay

Received 15 August 2016; Revised 11 December 2016; Accepted 14 December 2016; Published 31 January 2017

Academic Editor: Shuming Wang

Copyright © 2017 Ying Liu and Ya-Nan Li. 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.


When facing to make a portfolio decision, investors may care more about every portfolio’s performance on a return and risk trade-off. In this paper, a new low partial moment measurement that only punishes the loss risk is defined for selection variables based on L-S integral. Furthermore, a new performance measure for portfolio evaluation is proposed to generalize the Sharpe ratio in the fuzzy context. With the optimal performance criterion, a new parametric Sharpe ratio portfolio optimization model is developed wherein uncertain returns are presented as parametric interval-valued fuzzy variables. To make the proposed model easy to solve, we transform the fractional programming into an equivalent form and solve it with domain decomposition method (DDM). Finally, we apply the proposed performance measure into a portfolio selection problem, compare the computational results in different cases, and analyze the influence of different parameters on the optimal portfolio.