【作者】 姚元端；

【导师】 彭大衡； 胡宗义；

【作者基本信息】 湖南大学 ， 数量经济学， 2005， 硕士

【摘要】 随着经济、金融全球一体化和金融创新、金融技术进步日益加快,我国金融市场正在经历基础性和结构性变革,我国资本市场的也不断完善和发展,市场规模迅速扩大,投资机会和投资渠道不断增多,证券投资已经逐渐成为我国居民投资理财的一个重要渠道,投资组合理论也因此得到迅速普及。以1952年Markowitz发表《Portfolio Selection》为投资组合理论奠基标志,现代金融投资决策开始摆脱纯描述性研究和单凭经验操作的状态,而进入到了定量分析的高级阶段。半个多世纪来,国外金融投资数理模型的研究取得了许多杰出的成果,并逐渐与数理金融研究相结合,证券分析方法和证券投资数学模型的研究已经成为当前国际上研究金融市场的结合点和前沿。在这方面,我国的研究虽然在一些方面取得了进展,但整体而言,现代投资决策的动态数理模型研究还有限。本文在深入研究现代投资学和金融学等有关理论的基础上,对连续时间情形下的动态模型进行了较为系统的研究。 本文将投资者的风险偏好、收益约束和形成最优金融资产组合的置信水平相结合,构建了投资的最优动态资产配置模型,同时,在金融学意义上,对模型的最优解及其适用范围进行了研究与探讨,利用所建立的模型框架和分析方法进行最优消费投资策略的构造。 全文结合Markwitz和Sharpe的投资组合模型构建最优资产选择模型的思想方法,在Black-Scholes型金融市场设置下,分别用渐进Log收益率,投资机会来取代均值(Mean)指标,用在险价值(Value-at-Risk,VaR)和在险资本(Capital-at-Risk,CaR)来取代方差(Variance ,Var)指标,将经典的均值——方差(M-V)模型拓展到了连续时间金融市场,而且,推导出了这些模型的最优常数再调整证券投资策略,模型可以具体地应用于动态投资决策与管理实践中,并通过例子说明了这些模型。 第一章是绪论,说明了本文选题背景和国内外研究现状及本文的研究思路方法和主要内容。第2章通过对投资组合基本理论与基本模型的比较研究,探讨投资组合模型的构建机理。第3章则建立了基于风险约束的渐近Log-最优动态投资组合模型,讨论了约束条件的调整方法,使得动态模型可以方便地应用于实践。第4章研究了基于投资机会约束的最优动态金融资产配置模型,引进了在险资本(CaR)风险概念,详尽地讨论了最优解的各种情况,该模型可以得出一个与观察相一致的结论:在长期投资角度下,投资期越长,投资者持有风险资产的比例反而会增加。作为一个应用,第5章则利用所建立的模型,讨论了当已知具体的更多还原

【Abstract】 As our market of Securities develops in the direction of regulation and health, investment in securities is becoming a more and more important financial way of people. Using the way of quantitative and qualitative analysis, this article studies the market behavior of common investors from three micro layers of the financial market as follows: 1.common research on Portfolio mechanism; 2.mathematical model reasoning; 3.simulating calculation test of the market.Surrounding how to integrate the investment preference of people, the constraint of profit and the confidence level of the optimal portfolio, this paper establishes a dynamic asset allcation model of long-term investment.Meanwhile,this paper analyses and interpretes the best solution to the model and its scope of utility, and then, using the established model frame and analystic ways,this paper deals with optimal consuming investment strategies.Connecting with classic portfolio theories of building up the optimal asset allocation models and under the Black-Stoles financial market setting,this paper uses the progressive log profit rate or the constraint of investment chances to replace the mean in Markowitz mean-Var model, uses Value-at-Risk(VaR) or Capital-at-Risk(CaR) to replace the index of variance and extends the classic markowitz mean- VaR model to continuous-time financial market.Furthermore, this paper reasons out the best constant rebalanced Portfolio investment strategies and deals with best solutions in various situations and these solutions can be adapted to practice of dynamic investment strategies and management and can be illustracted.This paper is made up of 5 chapters as follows:Chapter Ⅰ is the preface, it briefly introduces the background of choosing this thesis and the current foreign and domestic research situation of this subject, and the basic researching way and contents are shown in this part.Chapter Ⅱ analyses the constructing mechanism of portfolio model through the comparative research of basic portfolio theories and basic models.Chapter Ⅲ establishes the progressive log-optimal dynamic portfolio model based on the constraint of risk and discusses the adjusting ways of constraint conditions.Chapter Ⅳ studies the optimal dynamic financial asset allocation model basedon the constraint of investment chance, and it brings into the risk concept of Capital-at-Risk(CaR) and detailly discusses various situations of the best solution It’s of the same importance that the model of this paper provides a conclusion ,which is in accordance with the observation, that is ,in the aspect of long-term investment, the longer the investment is ,the higher the rate of the CaR of the investors will be .As an adoption, using the established model, the 5th chapter discusses the constructing of the optimal dynamic consuming investment strategies,when the utility function is known.The renovations of this paper mainly are as follows.1.Using the basic idea of portfolio theory to set up four dynamic models of investment strategies.2.Making use of the established model to interpret to the relationship between the term and the rate of CaR of long-term investment.3.Using the established model to set up an optimal consuming investment strategy.更多还原