模糊环境下的投资决策及投资组合研究

【作者】 杨洋；

【导师】 肖辞源；

【作者基本信息】 西南石油大学 ， 应用数学， 2006， 硕士

【摘要】 投资研究从上世纪中期到如今，始终是众多学者的研究热点，它对国家、人民的经济生活起到了指导性作用，已有众多学者在经典理论下建立了许多投资模型，但是在实际应用中，许多数据得不到精确量化，所以许多经典模型往往只具有理论价值，而缺少实际的应用价值。由于未来的不可预知性，投资者常常只能基于经验和知识对未来资金流、贴现率等重要数据做出主观评价，于是本文引入模糊理论的方法对投资者在模糊环境下的投资决策进行进一步的研究。 本文综合应用模糊数学、最优化理论、数值计算、金融投资学、软件工程等学科的理论知识，在前人已有成果的基础上对投资方案的决策作了以下方面的研究： (1) 对于模糊数排序问题，根据风险投资具体情况引入了风险承受度参数λ，定义了模糊数的平均指数排序法，该法对金融数学中三角模糊数的排序问题特别适用。 (2) 提出了在模糊环境下的一种投资评价标准，分别对净现值和内部收益率两种指标进行了投资分析，用三角模糊数来表示资金流和贴现率，保证了信息的完整性，将三角模糊数转化为α截集形式，从而解得由三角模糊数表示的净现值以及内部收益率，对一系列待定投资方案进行排序并且分析怎样来选择可行的投资方案。 (3) 提出了预算限制概念，在该限制下选择组合投资。改进了前人提出的经典条件下的优化模型，对其进行模糊化，并加以预算限制条件，从而建立模糊线性规划模型，使得该模型不仅在理论上可行，而且在实际应用中更为合理。 (4) 在windows98／2000／ME／NT／NP操作系统平台上，应用数值计算软件包Matlab编制投资决策软件系统，将所有繁琐计算过程软件自动化，该系统主要实现基于模糊环境下决策者对投资方案可行性的决策并且能选择出合理的投资组合。更多还原

【Abstract】 From last mid-century to today, investment research has always been a hot issue, which has played a guiding role on both country and the people. Many scholars have established a lot of investment models under classical theory, but in practical applications, many data are not well exactly qualified, and therefore many classical models often only have a theoretical value and lack of practical application value. Due to the unpredictable nature of the future, investors who may make some subjective evaluations are often based on the experience and knowledge for the future cash flows, discount rate and other important data. So this thesis has introduced the fuzzy theory to the research of investment under fuzzy conditions.On the basis of the theory and knowledge of many branches such as fuzzy mathematics, optimization theory, numerical computing, financial investment science, software engineering, this thesis has made the following research based on the predecessors’ outcomes:(1) For ordering fuzzy numbers, this thesis introduced A which is an index represents the investor’s risk aversion, and defined a average index which can well cope with the triangular fuzzy numbers in finance risk conditions.(2) Presented an investment evaluation criteria, which would well analyzed both index of the Net Present Value and the Internal Rate of Return respectively, it used the triangular fuzzy numbers to represent the cash flows and the discount rate ensuring the integrity of the initial information, and also transformed the triangular fuzzy numbers into α -cuts, and therefore analyzed how to rank investments and how to choose a tangible investment project.(3)We has introduced the concept of budgetary constraint and selected the tangible investment portfolio, and also we improved the classic optimize modal which introduced by processor using fuzzy ways and set a extra restricted budget, and therefore constructed a fuzzy linear programming, so this model is not only theoretically feasible but also reasonable in practical application.(4) In windows98/2000/ME/NT/NP operating system platform, we used the mathematical software Matlab to set up investment decision-making system and let all the heavy calculations automation. It mainly carried out the investor’s decision-making about the feasibility of the investment projects and even select the reasonable investment portfolio.更多还原