A new risk criterion in fuzzy environment and its application
- 作者：Yanju Chen chen-yanju@163.com ; Yankui Liu ; yliu@hbu.edu.cn ; Xiaoli Wu wxl861@126.com
- 关键词：Risk measure ; Absolute semi-deviation ; Fuzzy portfolio optimization ; Fractional programming ; Pseudo-convexity ; Domain decomposition method
- 刊名：Applied Mathematical Modelling
- 出版年：2012
- 期刊代码：6_0307904x
- 类别：cp
- 出版时间：July, 2012
- 卷：36
- 期：7
- 页码：3007-3028
- 文件大小：324 K
摘要
Since the observed values of security returns in real-world problems are sometimes imprecise or vague, an increasing effort in research is devoted to study the properties of risk measures in fuzzy portfolio optimization problems. In this paper, a new risk measure is suggested to gauge the risk resulted from fuzzy uncertainty. For this purpose, the absolute deviation and absolute semi-deviation are first defined for fuzzy variable by nonlinear fuzzy integrals. To compute effectively the absolute semi-deviations of single fuzzy variable as well as its functions, this paper discusses the methods of computing the absolute semi-deviation by classical Lebesgue-Stieltjes (L-S) integral. After that, several useful absolute deviation and absolute semi-deviation formulas are established for common triangular, trapezoidal and normal fuzzy variables. Applying the absolute semi-deviation as a new risk measure in portfolio optimization, three classes of fuzzy portfolio optimization models are developed by combining the absolute semi-deviation with expected value operator and credibility measure. Based on the analytical representation of absolute semi-deviations, the established fuzzy portfolio selection models can be turned into their equivalent piecewise linear or fractional programming problems. Since the absolute semi-deviation is a piecewise fractional function and pseudo-convex on the feasible subregions of deterministic programming models, we take advantage of the structural characteristics to design a domain decomposition method to separate a deterministic programming problem into three convex subproblems, which can be solved by conventional solution methods or general-purpose software. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness of the solution method.