【作者】 张国；

【导师】 刘则毅；

【作者基本信息】 天津大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 正确的投资决策是建立在对收益率与风险的可靠预测之上的,而可靠的预测只能通过基于现实假定上的统计模型而得到。传统的证券组合投资研究,如Markowitz投资组合模型,大多采用正态分布来描述收益率变化的概率分布,然而在许多实证分析研究中,证券收益率经常具有“尖峰厚尾”现象,这是正态分布所不能描述的,然而稳定分布则能够描述金融数据中的这两个重要经验特征:厚尾性以及波动集聚性。由此,本文主要借助于John Nolan教授的稳定分布软件STABLE程序对稳定分布下的组合投资、概率准则下的投资组合问题以及稳定分布下中国股票收益率的VaR的计算等问题进行了研究。主要研究内容如下:首先,介绍了一元稳定分布以及多元稳定分布基本理论。其次,建立了稳定分布下证券投资组合模型的均值/绝对偏差模型,并在中国市场情况下,研究了模型的改进和模型的解法。再次,描述了正态分布下的概率准则投资组合问题,给出了允许卖空时最优解的解析表达式以及不允许卖空时求解最优解的方法;研究了稳定分布下风险资产的概率准则投资组合问题,描述了求解概率准则模型的同步扰动随机逼近算法,将深圳成分指数(SZSI)和上海综合指数(SHCI)作为风险资产进行实例分析,给出了求解概率模型最优解数值算法的具体步骤。最后,同传统正态分布下的VaR相比较,研究了稳定分布下中国股票市场的VaR计算,验证了稳定分布下VaR计算的可行性与可靠性。更多还原

【Abstract】 Right investment decision requires reliable predictions of return and risk, andreliable predictions can only be obtained if the underlying statistical model rests onrealistic assumptions. In the traditional portfolio researching, for example theMarkowitz portfolio model, the normal distribution was mostly applied to fit theprobability distribution of the security’s return rate. But in many practical researching,the financial data time serials represent the phenomenon of the heavy tail and excesskurtosis, which the normal distribution can’t describe. Stable laws are able to capturethe two main empirical characteristics that heavy-tailed and volatility clustering.Therefore, by means of John Nolan’s stable distribution analysis software—the stableprogram, some problems are discussed, which include portfolio with stabledistribution, the optimal portfolio selection of probability criterion, the VaR of stockreturns of China with stable distribution, etc.The main contents and results are as follows:Firstly, the basic theories of univariate stable distribution and multivariate stabledistributions are introduced.Secondly, the mean-absolute deviation model based on the stable distribution isbuilt and we modify the model and research its solution under the stock market ofChina.Thirdly, the optimal portfolio selection of probability criterion with normaldistribution is considered, the analytic representation of the optimal portfolio withshort selling allowed is obtained and the method for solving the optimal portfolio withno short selling allowed is given;The optimal portfolio selection of probabilitycriterion based on stable distribution for risky assets is considered and thesimultaneous perturbation algorithm for stochastic optimization is implemented tosolve the model. Regarded the Shenzhen Stock Sub-index (SZSI) and Shanghai StockComposite Index (SHCI) as risky assets, the portfolio model of probability criterion isbuilt and the steps of numerical method are given.Lastly, compare with the VaR with normal distribution, the VaR of stock returnsof China based on the stable distribution is discussed. The results show that thecalculation of the VaR is feasible and effective based on the stable distribution.更多还原