A Class of Fuzzy Portfolio Optimization Problems: E-S Models
A Class of Fuzzy Portfolio Optimization Problems: E-S Models
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DOI：
10.1007/978-3-642-13498-2_6
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发表时间：
2010-06
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影响因子：
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通讯作者：
Yankui Liu;Xiaoli Wu
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文献类型：
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作者：
Yankui Liu;Xiaoli Wu
本文将模糊变量的分布作为实际风险管理问题中的一个新准则，提出了一种新的模糊期望-分布模型(E-S)。由于离散度是由L-S(LebesgueStieltjes)积分定义的，一般模糊变量的离散度的计算是一个具有挑战性的问题，通常依赖于逼近格式和软计算。但对于经常使用的梯形和三角形模糊变量，扩散可以表示为关于模糊参数的二次函数。这些新的表示便于我们将所提出的E-S模型转化为其等价的参数规划问题。因此，在给定模糊参数的情况下，E-S模型变成了一个二次规划问题，可以用通用软件或常规优化算法来求解。最后，通过两个数值算例验证了所提出的建模思想。
This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is defined by Lebesgue-Stieltjes (L-S) integral, its computation for general fuzzy variables is a challenge issue for research, and usually depends on approximation scheme and soft computing. But for frequently used trapezoidal and triangular fuzzy variables, the spread can be represented as quadratic functions with respect to fuzzy parameters. These new representations facilitate us to turn the proposed E-S model into its equivalent parametric programming problem. As a consequence, given the fuzzy parameters, the E-S model becomes a quadratic programming problem that can be solved by general purpose software or conventional optimization algorithms. Finally, we demonstrate the developed modeling idea via two numerical examples.