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为了度量金融市场的不确定性,本文引入了模糊变量。假设资产收益率为模糊数,分别运用可信性均值和可信性绝对偏差度量投资组合的收益与风险。考虑到投资者偏好,分别提出了以收益最大化的均值-绝对偏差优化模型和以风险最小化的优化模型。基于可信性理论,将上述模型转化为线性规划问题,并运用旋转算法求解。通过实证研究,证明了该算法的有效性,并比较了两个模型在实际投资决策过程中的效率。结果表明,以收益最大化的均值-绝对偏差优化模型效率优于风险最小的优化模型。
In order to measure the uncertainty of the financial market, this paper introduces fuzzy variables. Suppose the rate of return on assets is fuzzy number, respectively, using the credibility of the average and credibility of the absolute deviation of the portfolio measurement of returns and risks. Taking into account the preference of investors, the optimal model of mean-absolute deviation and the optimization model of risk minimization are respectively proposed to maximize returns. Based on the credibility theory, the above model is transformed into a linear programming problem and solved by a rotation algorithm. The empirical research proves the effectiveness of the algorithm and compares the efficiency of the two models in the actual investment decision-making process. The results show that the efficiency-maximized mean-absolute deviation optimization model is better than the least-risk optimization model.