基于股票配对策略的动态资产配置研究

发布时间：2018-01-10 23:01

本文关键词：基于股票配对策略的动态资产配置研究　出处：《上海师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：配对交易最早是由华尔街交易员Jesse Livermore创造的交易策略.随着计算机技术的飞速发展,配对交易越来越广泛地被运用于金融市场中.2010年3月起我国证券市场相继开展了融资融券业务和股指期货业务,这为配对交易策略在我国证券市场中的实现提供了前提与基础.目前关于配对交易的研究主要有两类,一类是基于统计和数据挖掘方法实现配对交易,另一类则是基于方程方法实现配对交易.其中第一类的研究在应用层面更为广泛,但这一类的主要缺陷是无法通过配对标的的头寸数量来控制风险.所以本文研究了在配对价差满足O-U过程的条件下最优投资策略问题.与先前一些学者的研究内容不同,本文考虑了止损止盈策略.在第三章中,我们建立了最优投资策略所满足的HJB方程并在此基础之上给出了止损或止盈时方程的边界条件.但由此所建立的HJB方程很难求出解析解,因此我们运用了有限差分法求解.为了保证系数矩阵的半正定性,我们使用了广义网格的方法建立HJB方程的差分格式,将HJB方程近似为一个非线性方程组.之后,我们运用迭代法和预处理共轭梯度法(PCG)求解该方程组从而得出HJB方程的数值解.然后我们针对不同的参数情况对最优策略进行了数值分析.在第四章中,为了确保第三章中差分格式以及迭代算法的正确性,我们研究了差分格式的相容性,单调性,稳定性以及迭代算法的收敛性.在第五章中,我们进一步拓展了基于配对交易的最优策略模型.我们使用均值方差模型作为投资者的目标,同样考虑止损止盈策略,然后建立HJB方程并运用第三章中的方法求出了该方程的数值解.最后,我们进行了数值分析,在其他参数条件不变的情况下比较了第三章的最优策略与第五章中最优策略的差异性.
[Abstract]:Pairing was first created by Jesse Livermore, a Wall Street trader, with the rapid development of computer technology. Pairing transactions are more and more widely used in the financial market. Since March 2010, China's securities market has carried out margin trading and stock index futures business one after another. This provides the premise and foundation for the realization of pairing trading strategy in Chinese securities market. At present, there are two kinds of research on pairing transaction, one is based on statistics and data mining method to realize pairing transaction. The other is the equation-based method to achieve pairing transactions, the first kind of research is more widely used in the field of application. However, the main defect of this kind is that the risk can not be controlled by the number of positions of the matched target. Therefore, this paper studies the optimal investment strategy under the condition that the pairing spread satisfies the O-U process. The content is different. This paper considers the stop loss and stop gain strategy in Chapter 3. We establish the HJB equation satisfied by the optimal investment strategy and give the boundary conditions of the stop loss or stop gain equation on this basis. However, the HJB equation is difficult to find the analytical solution. In order to guarantee the positive semidefinite of the coefficient matrix, we use the generalized grid method to establish the difference scheme of HJB equation. The HJB equation is approximated as a nonlinear system of equations. We use the iterative method and the preconditioned conjugate gradient method (PCG). The numerical solution of the HJB equation is obtained by solving the equations. Then we give a numerical analysis of the optimal strategy for different parameters. In Chapter 4th. In order to ensure the correctness of the difference scheme and the iterative algorithm in Chapter 3, we study the consistency, monotonicity, stability and convergence of the iterative algorithm. In Chapter 5th, we study the consistency, monotonicity, stability and convergence of the iterative algorithm. We further extend the optimal strategy model based on paired trading. We use the mean variance model as the target of investors and consider the stop loss and stop earnings strategy. Then the HJB equation is established and the numerical solution of the equation is obtained by using the method in Chapter 3. Finally, we carry out the numerical analysis. The differences between the optimal strategy in Chapter 3 and the optimal Policy in Chapter 5th are compared under the condition that other parameters are invariant.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F832.51;F224

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