【作者】 刘树人；

【导师】 成央金；

【作者基本信息】 湘潭大学 ， 应用数学， 2002， 硕士

【摘要】 本文基于组合投资模型的特点，利用Kuhn-Tucker条件将其转化为线性互补问题，提出了求解高维数组合投资问题的转轴方法，并结合具体实例进行数值模拟得到了预期的结果，帮助投资者进行决策分析，从而理论联系实际，直接将理论应用到实践中。该方法的优点在于能够处理各投资项目之间的协方差矩阵为半正定的情形。在§1中，我们首先介绍了如何利用时间序列预测法估计证券的预期收益率和风险，然后以投资组合随机收益率的方差作为投资的风险度量，建立起投资组合模型。在§2中，我们利用非线性规划的重要理论成果—Kuhn-Tucker定理，给出了二次规划的最优性条件—线性互补问题。在§3中， 我们考虑到线性互补问题的特点，结合线性规划方法，把线性规划的单纯形法加以适当修改，提出了求解线性互补问题的转轴方法，接着引入协调正加矩阵的概念，研究了转轴算法的有限收敛性。在§4中，我们利用上述讨论的转轴方法求解投资组合模型，运行编写的C程序对给出的算例进行数值模拟，实践表明该方法是非常有效的。更多还原

【Abstract】 In this paper, it is discussed that the portfilio model can charge into Linear complementarity problem using Kucker-Tucker theorem, and we propose a pivoting method and present a method to solve the high-dimension portfolio problem. We also make some computationalExperimence .Our computing illustrates that our methods are efficient and reliable , which can help the investor make decision in practice. An advantage of this method is that it can be applied when the covariance matrix of the invested projects is positive semi-definite.In Ⅰ,it is discussed how to estimate the profit expection and risk of portfolio by time series, and that the portfolio investment model can be made by the variance of portfolio selection random profit.In Ⅱ, we obtain the optimality conditions for quadratic programming—Linear complementarity problem by Kuhn-Tucker theorem.In Ⅲ, first a pivoting method for linear complementarity problem can be proposed by its feature and the simplex algorithm for Linear programming. Second we give copositive-plus matrix and invest the finite convergence analysis.In Ⅳ, we present the pivoting method to solve the portfolio selection model, and also show some computational experimence by C program.The result of numerical experiment is satisfactory.更多还原