数学规划论文马科维兹模型及其改进.doc

马科维兹模型及其改进 摘要： 证券投资者通过把资金投资一种或几种收益较高的证券以获得最大限度的收益，但是收益与风险是相辅相成的，高收益必然包含高风险.因此投资者需要选择若干证券加以组合，以分散其投资风险，尽可能的实现低风险和高收益.1952年马科维兹理论的提出开创了金融理论的先河，改变了人们经验投资的传统，使投资组合更加科学性和广泛性. 马科维兹模型实质是在不损失收益率的条件下最大限度地分散投资风险，能够指导人们科学地选择证券投资组合以实现效益最大化.本文主要介绍马科维兹理论及模型的建立以及最新的研究进展，并在此基础上提出了三种模型目标函数的改进方案：引进决策系数、引进厌恶偏好程度及目标规划，并对此进行了对比分析. 三种改进方案都能使原本的多目标规划转化为单目标规划，并且都有其适用的范围：决策系数适用于比较两种不同投资组合的优劣；引进偏好程度能够在未给定预期收益及预期风险下定制个人的最优投资组合；利用目标规划能够使个人选择尽可能的达到自己预期的最优投资组合. 关键字：马科维兹模型；投资组合；数学规划 Markowitz model and its improvement Abstract: Securities investors get Investment income by investing one or more higher-yielding securities.But benefits and risks are complementary to each other, high-yield inevitably contains high risk.So investors need to choose a number of securities portfolio to diversify risk and get low risk and high yield. Markowitz, who created?Markowitzs?Portfolio?Theory, changed the convention of investment and make portfolio?theory more scientific and comprehensive. Markowitz model essential is under the condition of no loss of yield maximum disperse investment risk,which can direct people to choose science portfolio to achieve the benefit maximization.This paper introduces Markowitzs?Portfolio?Theory and ?puts forward three models on the basis of the objective function:decision coefficient,disgusting appetite and objective programming. Three kinds of improve models can make the multi-objective programming transformed into single objective programming and they have different applicable scopes. First,decision coefficient can compare the merits of the two different portfolios.Second,disgusting appetite is able to customize the individual optimal portfolio without expected profit and expected risk.Last,objective programming can make people get the optimal portfolio. Key words: Markowitz model; Investment portfolio; Mathematical programming 目 录 摘要 1 引言 4 1.证券投资 5 2.马科维兹模型 6 2.1马科维兹投资组合理论基础 6 2.1.1模型的假设 6 2.1.2预期收益 7 2.1.3预期风险 7 2.2证券投资的有效组合 9 2.2.1无差异曲线 10 2.2.2有效市场边界 11 2.2.3最优投资组合的选择 12 2