CVaR Reduced Fuzzy Variables and Their Second Order Moments
CVaR Reduced Fuzzy Variables and Their Second Order Moments
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DOI：
10.22111/ijfs.2015.2111
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发表时间：
2015-10
影响因子：
1.8
通讯作者：
X. Bai;Yankui Liu
中科院分区：
文献类型：
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作者：
X. Bai;Yankui Liu
基于正则模糊变量的可信风险值(CVaR)，我们提出了一种新的2型模糊变量CVaR约简方法。减少的模糊变量由参数可能性分布来表征。我们为常见的约化模糊变量的平均值和二阶矩建立了一些有用的解析表达式。还讨论了二阶矩相对于参数的凸性质。最后，我们将二阶矩作为一种新的风险度量，并开发了平均矩模型来优化模糊投资组合选择问题。根据二阶矩解析公式，平均矩优化模型等价于参数二次凸规划问题，可用通用优化软件求解。数值实验中报告的求解结果证明了所提出的优化方法的可信度。
Based on credibilistic value-at-risk (CVaR) of regularfuzzy variable, we introduce a new CVaR reduction method fortype-2 fuzzy variables. The reduced fuzzy variables arecharacterized by parametric possibility distributions. We establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. The convex properties of second order moments with respect to parameters are also discussed. Finally, we take second order moment as a new risk measure, and develop a mean-moment model to optimize fuzzy portfolio selection problems. According to the analytical formulas of second order moments, the mean-moment optimization model is equivalent to parametricquadratic convex programming problems, which can be solved by general-purpose optimization software. The solution results reported in the numerical experiments demonstrate the credibility of the proposed optimization method.