Optimizing fuzzy portfolio selection problems by parametric quadratic programming

This paper develops a robust method to describe fuzzy returns by employing parametric possibility distributions. The parametric possibility distributions are obtained by equivalent value (EV) reduction methods. For common type-2 triangular and trapezoidal fuzzy variables, their reduced fuzzy variabl...

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Vydané v:Fuzzy optimization and decision making Ročník 11; číslo 4; s. 411 - 449
Hlavní autori: Wu, Xiao-Li, Liu, Yan-Kui
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.12.2012
Springer Science + Business Media B.V
Springer Nature B.V
Predmet:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Credibility
Decision making
Equivalence
Expected values
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Integrals
Mathematical analysis
Mathematical Logic and Foundations
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Portfolio management
Probability Theory and Stochastic Processes
Quadratic programming
Random variables
Representations
Studies
Parametric possibility distribution
Portfolio selection
Moment
Parametric programming
Reduced fuzzy variable
ISSN:1568-4539, 1573-2908
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Shrnutí:This paper develops a robust method to describe fuzzy returns by employing parametric possibility distributions. The parametric possibility distributions are obtained by equivalent value (EV) reduction methods. For common type-2 triangular and trapezoidal fuzzy variables, their reduced fuzzy variables are studied in the current development. The parametric possibility distributions of reduced fuzzy variables are first derived, then the second moment formulas for the reduced fuzzy variables are established. Taking the second moment as a new risk measure, the reward-risk and risk-reward models are developed to optimize fuzzy portfolio selection problems. The mathematical properties of the proposed optimization models are analyzed, including the analytical representations for the second moments of linear combinations of reduced fuzzy variables as well as the convexity of second moments with respect to decision vectors. On the basis of the analytical representations for the second moments, the reward-risk and risk-reward models can be turned into their equivalent parametric quadratic convex programming problems, which can be solved by conventional solution methods or general-purpose software. Finally, some numerical experiments are performed to demonstrate the new modeling ideas and the efficiency of solution method.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-012-9126-9