The mean-absolute deviation portfolio selection problem with interval-valued returns

In real-world investments, one may care more about the future earnings than the current earnings of the assets. This paper discusses the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval valued, the gain of returns is in...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 14; pp. 4149 - 4157
Main Author: Liu, Shiang-Tai
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 15.05.2011
Elsevier
Subjects:
Absolute deviation function
Deviation
Economics
Exact sciences and technology
Gain
Global analysis, analysis on manifolds
Intervals
Investments
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Portfolio selection
Risk
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Transformations
Two-level program
49M
Two-level program
Risk
Portfolio selection
90C
Absolute deviation function
Lower bound
Finance
Optimization method
Duality
Mathematical transformation
Selection problem
Upper bound
Numerical analysis
Applied mathematics
Mathematical model
Mathematical programming
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In real-world investments, one may care more about the future earnings than the current earnings of the assets. This paper discusses the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval valued, the gain of returns is interval valued as well. According to the concept of the mean-absolute deviation function, we construct a pair of two-level mathematical programming models to calculate the lower and upper bounds of the investment return of the portfolio selection problem. Using the duality theorem and applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a conventional one-level mathematical program. Solving the pair of mathematical programs produces the interval of the portfolio return of the problem. The calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on the greater the potential return.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.03.008