基于非参数贝叶斯方法的资产配置

发布时间：2018-05-01 07:08

本文选题：资产配置 + 非参数贝叶斯　；参考：《华中科技大学》2012年博士论文

【摘要】：资产配置是投资决策的首要环节,并对投资绩效产生最为重要的影响。但是,资产配置研究困难很大。一方面,资产的风险收益特征众说纷纭,而不同的资产收益生成过程下的资产配置结果差异很大。另一方面,投资者拥有的关于资产收益生成过程形式和参数的信息是不完全,如果忽视参数不确定和模型不确定,会导致投资决策处于次优状态。本文针对这两大难题,建立离散时间下非参数贝叶斯静态资产配置的分析框架。针对风险资产收益率分布不确定和金融市场市场状态不确定,将Dirichlet过程的扩展形式Dirichlet过程混合模型和分层Dirichlet过程隐马尔可夫模型引入风险资产收益随机波动率模型,从理论上研究了拥有不完全信息的投资者的静态资产配置间题。用MCMC方法推断随机波动率模型,再用Monte Carlo方法从预测分布中抽样近似得到资产配置问题的最优解。用Dirichlet过程混合正态模型描述风险资产随机波动率模型测量方程扰动项的分布,建立Dirichlet过程混合随机波动率模型,用MCMC方法推断该模型,推导了多期收益率预测值函数期望值的计算方法,并用该方法求解相应的资产配置问题。以中国金融市场数据使用模拟方法分析了不同投资期期望效用最大化的投资者在Dirichlet过程混合随机波动率模型下的贝叶斯最优资产配置。研究结论表明,相对于参数随机波动率模型来说,最优风险资产配置比例整体出现下移,同时随着投资期限的增加,风险资产比重呈下降趋势。引入Dirichlet过程描述分布不确定后,投资者对风险资产收益率的分布预测包含了与之对应的新的额外不确定性,而且随投资期限的增长而加大。效用成本的计算表明,对于极度厌恶风险的投资者来说,极度厌恶风险的2.5年投资期的投资者忽略分布不确定导致的效用损失约为1.7%。金融市场存在结构变换的特征,为此进一步将分层Dirichlet过程隐马尔可夫转换模型引入Dirichlet过程混合随机波动率模型,建立分层Dirichlet过程状态转换随机波动率模型,用MCMC方法分析了模型的推断,然后求解相应的资产配置问题。研究结论表明,相对于参数SV模型来说,最优风险资产配置比例整体出现下移,同时随着投资期限的增加,风险资产比重呈下降趋势,但整体下移的幅度小于Dirichlet过程混合随机波动率模型下的风险资产配置。引入Dirichlet过程描述市场状态的不确定性后,投资者为了规避状态不确定性,产生对风险资产的对冲需求。效用成本的计算表明,对于极度厌恶风险的2.5年投资期的投资者来说,忽略市场状态的不确定性和分布不确定导致的效用损失约为2.2%。进一步的,投资者会以战略资产配置为基准,在不同市场条件下及时调整资产配置比例,以获取更高的收益。建立投资机会集为分层Dirichlet过程状态转换随机波动率模型下的波动择时决策,并应用于2006年3月末至2011年6月末共21个季度的资产配置。与开放式基金资产配置带来的财富变动比较显示,随机波动率模型下的波动择时能改进基金资产配置的绩效,而考虑了投资机会集分布不确定性的分层Dirichlet过程状态转换随机波动率模型下的波动择时能进一步提高资产配置带来的收益。
[Abstract]:Asset allocation is the first link of investment decision - making , and has the most important influence on investment performance . However , asset allocation research is very difficult . On the one hand , asset allocation results are different . On the other hand , investors own information about the form and parameters of asset returns .
In this paper , the stochastic volatility model of risk asset returns is introduced from the mixed model of the Dirichlet process and the hidden Markov model of the layered Dirichlet process . The stochastic volatility model is inferred from the theory . The stochastic volatility model is inferred from the MCMC method , and then the optimal solution of the asset allocation problem is obtained from the prediction distribution by Monte Carlo method .
The stochastic volatility model of risk assets is described by the mixed positive state model with Dirichlet process . The stochastic volatility model is established by using the method of MCMC .
In this paper , the characteristics of structural transformation in financial markets are introduced . To this end , the stochastic volatility model is introduced into the Dirichlet process by using the hidden Markov transition model of the layered Dirichlet process . The stochastic volatility model is established by the MCMC method , and the corresponding asset allocation problem is solved .
Further , investors will adjust the proportion of asset allocation in time under different market conditions based on strategic asset allocation to obtain higher returns . The establishment of investment opportunities set is an alternative time - making decision under the model of stratified Dirichlet process state transition stochastic volatility model , and is applied to asset allocation in 21 quarters from the end of March 2006 to the end of June 2011 . Compared with the wealth change brought by the open - end fund asset allocation , the volatility option under the stochastic volatility model can improve the performance of the asset allocation of the Fund .

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F830.59;F224

【参考文献】