Abstract
Since asset returns have been recognized as not normally distributed, the avenue of research regarding portfolio higher moments soon emerged. To account for uncertainty and vagueness of portfolio returns as well as of higher moment risks, we proposed a new portfolio selection model employing fuzzy sets in this paper. A fuzzy multi-objective linear programming (MOLP) for portfolio optimization is formulated using marginal impacts of assets on portfolio higher moments, which are modelled by trapezoidal fuzzy numbers. Through a consistent centroid-based ranking of fuzzy numbers, the fuzzy MOLP is transformed into an MOLP that is then solved by the maximin method. By taking portfolio higher moments into account, the approach enables investors to optimize not only the normal risk (variance) but also the asymmetric risk (skewness) and the risk of fat-tails (kurtosis). An illustrative example demonstrates the efficiency of the proposed methodology comparing to previous portfolio optimization models.
Original language | English |
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Pages (from-to) | 2139-2156 |
Number of pages | 18 |
Journal | Journal of Intelligent and Fuzzy Systems |
Volume | 30 |
Issue number | 4 |
DOIs | |
Publication status | Published - 10 Mar 2016 |
Externally published | Yes |
Keywords
- fuzzy multi-objective linear programming (FMOLP)
- fuzzy sets
- higher moments
- marginal impacts
- Portfolio selection