【作者】 葛瑜；

【导师】 黄南京；

【作者基本信息】 四川大学 ， 应用数学， 2004， 硕士

【摘要】 在资本市场关于投资和融资决策的研究，自组合投资理论诞生以来受到多方的关注，发展迅速，1990年诺贝尔经济学奖获得者Harry M.Markowitz用科学的语言，严格表达了“不要把鸡蛋放在一只篮子里”这句古老谚语要传达的思想，并且利用数学工具建立了证券组合投资理论的概念、理论和可以在计算机上操作的方法，奠定了组合投资理论的基础。William Sharpe在Markowitz理论的基础上提出了资本资产定价模型(CAPM)，引入β系数来度量公司的系统风险，建立了证券期望收益率和它的β系数之间的关系，为投资学提供了理论基础．使投资组合问题的研究上了一个新台阶，而CAPM也成为现代金融财务学中研究金融风险投资的一个重要分析方法。而Miller和Modigliani建立了一套有关财务决策的理论——MM理论，专门研究财务杠杆作用、企业价值问题，指导企业融资。 而实际中的市场由于具有很多不确定的因素，往往无法对资产的性质给出确切的描述。为此我们对资产的预期收益率给出在一定精度范圈内的估计，用模糊数来描述其预期收益率，使模型更具现实意义。 本文将讨论两种具有模糊预期收益率的证券组合投资选择模型，首先利用对称三角模糊数的约束满意度，假定在投资风险不大于某给定值的情况下，如何确定投资比例，使收益最大；其次讨论企业在融资条件下，面对优良资产和普通资产，该如何确定组合投资比例，使得在确定的收益率下，风险最小；而当融资发生变化时，企业的投资比例又将如何变化。更多还原

【Abstract】 The study of investment and financing decision-making in captial market attract everyone’s attention after the naissance of portfolio investment theory and take a rapid development.Using mathematics, Harry M.Markowitz, the economics Nobel Laureate in 1990, expressed strictly the saying " don’t put eggs in one basket " with scientific words, upbuilt the conception and theory of portfolio optional, and found operable method in computer, so, the foundation of portfolio selection was founded. William Sharpe brought Markowitz’s theory forward and advanced Capital Asset Pricing Model (CAPM). Purtherly, using coefficient β to measure system risk of the firm, he established connection between negotiable securities expected return rates and its β coefficient, laid a foundation of investment, upgraded the study of portfolio selection to a new highness, as a result, CAPM become a important analysis method of finance risk investment.Miller and Modigliani set up a theory about financing decision-making MM theory to research finance leverage and corporation merit and to guide corporation makeing decision about financing.In fact we can’t describe accurately the character of captial firmly because of many dubious factors in negotiable securities market. So we give a estimate for captial expectation yield and use fuzzy number to describe its expected return rates, which make the model more significant.In this paper we focus on two fuzzy-linear program models of portfolio investment in which expected return rates is fuzzy numbers.Firstly, using thesatisfaction of constraints of symmetry triangle fuzzy number and assuming the risk is not bigger than a given number,we selecte a investment proportion to make return rate maximal. Secondly, we discuss, when return rates is a given number, how to make decision on restriction borrowing rate with superior assets for firms to make risk minimal. Furthermore, when borrowing rates vary, how to change its investment proportion.更多还原