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多目标规划最优化数学模型在组合投资中的应用
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Abstract:
投资者将资金以特定比例分别投放于一篮子有价证券的行为就可以构建一个投资组合，证券投资的收益特性和风险特性使得证券投资组合管理构成了现代投资决策理论非常重要的一部分。本文以现代投资理论重要基石——马科维茨的均值–方差理论为基础，简化假设投资者都追求利益最大化和风险最小化，首先简要介绍了多目标规划初等数学模型，然后将其与证券领域里的有关指标有机结合建立了在证券组合投资里的多目标规划模型，引入风险偏好系数，将其优化为更便于计算的单目标规划模型，最后代入搜集到的有关数据运用Matlab进行求解，满足了不同风险偏好投资者的不同需求。
The behavior of investors investing funds in a certain proportion of a basket of securities can form a portfolio investment. The income characteristics and risk characteristics of securities investment make securities portfolio management an important part of financial management and investment decision-making. This article is based on Markowitz’s Mean-variance Theory—an important cornerstone of modern investment theory and it simplifies the assumption that investors are pursuing the maximization of profits and the minimization of risks. First, it briefly introduces the elementary mathematical model of multi-objective programming, and then it organically combines the relevant indicators in the securities field so we can establish a multi-objective programming model in portfolio investment, introduce a risk preference coefficient, optimize this model into a single-objective programming model which is more convenient to calculate, and finally extract the collected data into it to solve the problem with Matlab. The model could meet the different needs of investors with different risk preferences.
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