最优风险资产组合中的数学模型及其推导
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重庆大学经济与工商管理学院

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重庆大学重点课程建设项目(项目编号:201805054)


Mathematical Model and Its Derivation in Optimal Risk Portfolio
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School of economics and Business Administration Chongqing University

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Key course construction project of Chongqing University (Project No.: 201805054)

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    摘要:

    现代证券投资理论与方法中,最优风险资产组合是最重要的核心概念之一。本文主要研究证券组合选择中最优风险资产组合概念形成过程中的数学机理并进行数学推导与求解。首先利用数学分析的方法构建对应关系,即将证券组合的风险、收益与平面坐标系的数对建立一一对应关系,并利用代学方法在这些数对中定义一个序关系。再从解析几何的角度,利用二维平面中二次曲线的相关性质,通过分析二次曲线簇的交点坐标,构建符合资产组合理论相关条件的数学方程组,然后进行数学推导与求解。最后通过分析二元证券组合的投资机会集的数学模型,确定了二元证券组合中的最优风险资产组合的数学表达式,并以此方法推广到了多元证券组合的情形。

    Abstract:

    In modern securities investment theories and methods, the optimal risk portfolio is one of the most important core concepts. This paper mainly studies the mathematical mechanism of the formation of the concept of the optimal risk portfolio in portfolio selection and makes mathematical derivation and solution. First of all, we use the mathematical analysis method to construct the corresponding relationship, that is, the risk, return of portfolio and the number pairs of plane coordinate system to establish one-to-one correspondence, and use the algebraic method to define an order relationship among these number pairs. Then, from the perspective of analytic geometry, using the relevant properties of conic in two-dimensional plane, through the analysis of the intersection coordinates of quadric clusters, the mathematical equations that meet the relevant conditions of portfolio theory are constructed, and then mathematical derivation and solution are carried out. Finally, by analyzing the mathematical model of the investment opportunity set of the binary portfolio, the mathematical expression of the optimal risk portfolio in the binary portfolio is determined, and this method is extended to the case of multiple portfolio.

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  • 收稿日期:2020-01-13
  • 最后修改日期:2020-03-02
  • 录用日期:2020-03-02
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