指数跟踪下的稳健稀疏投资组合模型

发布时间：2018-04-26 12:54

本文选题：稳健稀疏投资组合 + 指数跟踪　；参考：《北京交通大学》2015年硕士论文

【摘要】：在指数跟踪中,跟踪误差衡量了股票市场的指数和投资组合权重之间所表现出来的差异.对于投资组合选择的问题,提出了很多优化方法,目的是为了通过寻找最优投资组合来减少跟踪误差.本文,在指数跟踪投资组合模型中,我们使用P2范数和lp(0p1)范数惩罚相结合的方法以期在指数跟踪中得到一个稳健的稀疏的投资组合.这里,l2范数惩罚的目的是为了对超定系统施加光滑从而减轻由高度相关变量带来的影响,因此有更好的样本外表现；通过lp(0p1)范数惩罚得到稀疏性来解决交易费的问题.在模型中,我们明确加入非负约束条件,即现实中的卖空限制.lp(0p1)范数惩罚项是非凸、非Lipschitz的,会带来计算上的复杂.为此,我们采用光滑投影梯度法(SPG)来求解这个稳健稀疏的投资组合模型.我们发现用SPG算法求解时至少会产生一个聚点,且任何一个由SPG法产生的聚点都是Clarke意义下的稳定点.本文中,这个方法被应用到了两个真实的股票指数：标普500和罗素3000,并且发现我们的lp2范数和lp(0p1)范数惩罚下的投资组合模型优于其他的方法.
[Abstract]:In index tracking, the tracking error measures the difference between the index and the portfolio weight of the stock market. To solve the problem of portfolio selection, many optimization methods are proposed to reduce the tracking error by finding the optimal portfolio. In this paper, in the exponential tracking portfolio model, we use the combination of P2 norm and lp0 p1) norm penalty method in order to obtain a robust and sparse portfolio in exponential tracking. Here the purpose of L2 norm penalty is to smooth the overdetermined system so as to reduce the influence brought by the highly correlated variables, so it has better performance outside the sample; the problem of transaction cost can be solved by obtaining sparsity through lp0 p1) norm penalty. In the model, we explicitly add non-negative constraints, that is, the real short-selling restriction. Lp0 p1) norm penalty term is non-convex, non-, which will lead to computational complexity. For this reason, we use the smooth projection gradient method (SPG) to solve this robust and sparse portfolio model. We find that at least one accumulation point can be generated by using SPG algorithm, and any accumulation point generated by SPG method is a stable point in the sense of Clarke. In this paper, this method is applied to two real stock indices, S & P 500 and Russell 3000, and it is found that our portfolio model with lp2 norm and lp0p1) norm is superior to other methods.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.59;F224

【共引文献】