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首页> 外文期刊>Journal of Applied Mathematics and Computing >Mean-variance models for portfolio selection with fuzzy random returns
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Mean-variance models for portfolio selection with fuzzy random returns

机译：具有模糊随机返回的组合选择的平均值模型

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摘要

This paper develops two novel types of mean-variance models for portfolio selection problems, in which the security returns are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. In the proposed models, we take the expected return of a portfolio as the investment return and the variance of the expected return of a portfolio as the investment risk. We assume that the security returns are triangular fuzzy random variables. To solve the proposed portfolio problems, this paper first presents the variance formulas for triangular fuzzy random variables. Then this paper applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to nonlinear programming ones. Due to the reduced programming problems include standard normal distribution in the objective functions, we cannot employ the conventional solution methods to solve them. To overcome this difficulty, this paper employs genetic algorithm (GA) to solve them, and verify the obtained optimal solutions via Kuhn- Tucker (K-T) conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed models and methods.
机译：本文开发了两种新颖类型的组合选择问题的平均方差模型，其中假设安全返回的特征是具有已知可能性和概率分布的模糊随机变量。在拟议的模型中，我们将投资组合的预期回报作为投资回报以及投资组合的预期回报作为投资风险的差异。我们假设安全返回是三角形模糊随机变量。为了解决拟议的投资组合问题，本文首先介绍了三角形模糊随机变量的方差公式。然后，本文将方差公式应用于所提出的模型，以便可以将原始产品组合问题减少到非线性编程。由于减少的编程问题包括目标函数中的标准正态分布，我们不能采用传统的解决方案方法来解决它们。为了克服这种困难，本文采用遗传算法（GA）来解决它们，并通过Kuhn-tucker（K-T）条件来验证所获得的最佳解决方案。最后，提出了两个数值例子以证明所提出的模型和方法的有效性。

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