【作者】 赵宁；

【导师】 李兴斯； Winston T Lin；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2012， 博士

【摘要】 投资组合问题在现代金融研究中占有重要地位,资本资产定价理论一直被认为是现代金融的核心内容之一,该理论从诞生之初至今已经经历了多个阶段的改进和变化,论文将以资本资产定价理论中的三方面问题为中心展开。首先,文章针对投资前期的市场选择问题,提出了以区域证券指数的联合波动情况代表市场因素变化的思路,建立了更加完备可信的市场因素。以此为基础所提出的Copula熵的概念,用以作为市场内部相关程度的衡量指标,以评估市场内部风险。通过对比分析Copula熵、相关系数及互信息,证明了Copula熵在度量相关度问题上的有效性及优势。数据试验中,以Copula熵为衡量指标度量了三大经济区域市场内部风险的时变性及结构差异性,以经济理论对分析的有效性进行了验证。第二,针对投资组合问题中的基金投资问题,提出了两阶段分析法：基金成分股联合波动分析以及基金组合分析。根据所建立的联合熵优化模型推导出针对不同情况的求解方法：联合熵对偶法和Copula熵数值法。论文将Jayness极大熵优化理论进行扩展,借鉴熵优化问题的对偶方法推导出最大联合熵及最小联合叉熵的优化问题求解方法。通过Copula熵与熵理论之间的联系,建立了联合熵与Copula熵之间的转化关系,提出了基于Copula熵的求解方法。利用Copula函数的构建思想将熵优化扩展到多元的情况,拓宽了熵理论在投资组合问题中的适用范围。由于基金等封装类的金融产品在我国属于新兴金融产品,缺少其本身的历史数据作为投资参考,该方法可以帮助投资者通过成分股信息分析基金组合,并构建适当的投资策略。最后一部分,文章针对资本资产定价模型中的投资期限问题提出了贝叶斯Copula估计方法,用以获得参数系统风险值与投资期限比的后验分布。在样本数据相关性明显存在的有力证据下,使用半相依回归(Seemingly Unrelated Regressions, SUR)替代普通估计方法进行参数估计；使用贝叶斯Copula估计替代原有贝叶斯估计方法进行了贝叶斯估计。半相依回归的使用主要用以考虑残差之间相关性对参数的影响,贝叶斯Copula方法将基于Copula函数的联合函数作为似然函数用以获得后验分布。数据试验分析了6个工业产业证券收益所受系统风险的影响与其投资期限比之间的关系,并对其进行了灵敏度分析。更多还原

【Abstract】 Investment portfolio is taken at the foremost position in the financial research and the capital asset pricing model is considered as one of the modern financial core contents. The CAPM keeps developing from the moment it born through many years. My dissertation includes three issues.First of all, the dissertation proposes the method which builds the market factor with joint distribution of the local stock index before we choose the investment field. The method solves the problem and we can build a market factor completely. We define the copula entropy which is considered as the measure index of correlation and the risk within the market. Comparing copula entropy with correlation coefficient and the mutual information, we can find that copula entropy is reasonable and has many advantages about measuring dependence. The copula entropy is used as the correlation index to measure the time-varying characteristics of the correlation and the risk within the market. In economic theory analyses, we also find out that the copula entropy is very significant.Second, we build the joint entropy optimization model to solve the fund investment portfolio, in which we propose two steps approach:constituent stocks analysis and fund portfolio analysis. There are two methods to solve the different joint entropy optimization models named dual joint entropy approach and copula entropy approach. We extend Jaynes’s maximization entropy principle. The dual theory is taken to get the solution of both the maximum joint entropy model and the minimum relative joint entropy model. The ideas of the copula entropy let us to transfer the joint entropy model to copula entropy model in entropy optimization problem. The copula entropy approach is proposed. The application to the fund portfolio is broadened. The packaged financial product such as the fund investment is still the new financial product and the history data are probably limited in China. The method we propose can build the possible strategy base on the constituent stocks of the fund.The last part of the dissertation, we propose the Bayesian copula estimation to get the posterior distribution of the parameters of the system risk beta and the investment horizon lambada. We find out the data are correlated each other strongly and choose Seemingly Unrelated Regressions method to get the result of the parameter estimation. The Bayesian copula estimation is chosen to consider the correlation of the data instead of regular Bayesian estimation. The reason we chose SUR is concerning the affect of the correlation of residuals and the Bayesian copula estimation using copula function as the likelihood function is proposed with the similar argument. The experiment analyzes the interaction of the system risk and the investment horizon in six different industries.更多还原