组合投资的数学模型

Model of the assembled investment

为了研究能使风险最小、收益最大的最优组合投资问题，首先建立了多目标规划模型，并利用约束法将该多目标规划问题转化为单目标规划问题．用单纯形法求解，得出在给定风险损失率下的最大收益率，并根据这些数据拟会风险收益曲线（该问题的有效解集的有效边界）．为了寻求最优组合投资方案，给出一种确定无差异曲线的方法，该无差异曲线能体现投资者决策准则．无差异曲线与风险收益曲线的公切点所对应的组合投资方案即为所寻求的最优组合投资方案．

For the study of the best assembled investment with the most earnings and the lest risk, a model of Multiobjective project is built and is changed into a simple target project by the restriction methed. After using the simplex method to solve the project, the most earning rate is worked out at a certain loss rate with risk. And then the datum above smooth the curve of the earning rate and the loss rate with risk. (The curve is the efficient boundary of the efficient solution set. ) In order to find the best scheme of the assembled investment, a method is provided to get the zero difference curve, which can show the decision rule of an investor. The scheme corresponding to the point of tangency on the two curves above is the best scheme of the assembled investment .