模糊数在投资组合优化中的应用研究及实证分析  

Portfolio Model and Analysis Based on Fuzzy Coefficients

作　　者：李春泉[1,2] 刘新平[2] 金检华[1,2] 

机构地区：[1]西南石油大学理学院,四川南充637001 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《数学的实践与认识》2010年第22期1-9,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(40271037)

摘　　要：采用模糊数处理不确定性信息.以模糊期望收益率最大为目标函数,使总的风险不高于给定的模糊数,建立了一种新的模型.在给定的截集下,期望收益率转化为区间数,目标函数转化为对该区间数的下限求最大值.基于模糊数大小的概率比较,从而将模糊优化模型转化为不等式约束下的线性规划模型.利用Matlab编程可解得其最优解.最后通过实例分析,验证该模型的可行性.In this paper,the portfolio selection problem is discussed from the viewpoint of fuzziness.Take the expected rates of security return as the objective function,and let the risks are not higher than the given fuzzy numbers.The new model is proposed.Based on the given cut set,the expected rates of security return is transformed to the intersection number and the objective function is transformed to the maximum value for its lower limit.Through the comparison beween trigangular mumbers,the fuzzy optimized model is transformed to the linear programming model under the inequality restraints.The optimal solution is solved by using matlab.Finally an example is given to illustrate that the new models can be used efficiently to solve portfolio selection problems.

关 键 词：投资组合模型 模糊数 模糊期望收益率 证券市场 

分 类 号：F224[经济管理—国民经济] F830.59