基于均值方差模型的加权半方差模型理论分析和实证研究-应用数学专业论文.docx

The The Theory Analysis and Empirical Research of the Weight Semi—variance Risk Measuring Portfolio Model Based on Mean Value—variance Model ABSTRACT In the first part，the beginning and development of modern portfolio theory is introduced，especially in China，and research 011 how to measure portfolio risk and investment returns，and then introduce some portfolio models based on the methods of measuring risk and returns． In the second part，it is started how to choose stocks and shares and how to optimize portfolio among selected stocks and shares in order to CUt down risk and obtain the highest returns．Under varied conditions，mathematical models are constructed which quanti tatively analyses portfolio risk and returns，then analyze the efficient frontier feature of the portfolios，especially analyze how to optimize portfolio when the risk matrix is singular covariance．Optimum portfolios are given by analyzing them quantitatively．Thus，maximum returns are achieved with acceptably expected investment risk，or minimum risk is obtained with given expected rate of portfolio returns． Finally，risk degree can not be indicated actually in practice by variance based on Markowitz mean—variance model．Semi—Variance risk measuring model only consider the part under the expected returns．Risk bias toe胁cient iS introduced． Stock certificate price has a Partial mutation，but from a long period of time the variety of the stock certificate price has the attribute of whole consecution，this paper quote their estimated value by using“partially integral mean value’’method in times series，then weight semi-Variance risk measuring portfolio model is established based on semi·Variance risk measuring model．By analysing a settled quantity of data empirically，the improved model is better then others．A strategy of portfolio investment based on an improved immune—genetic algorithm is presented； the result of emulation indicates that it iS linear between the lOSS of risk and the reward of risk．It achieves