Research On Dynamic Asset Allocation Based On Stock Matching Strategy

Pair trading is the trading stratrgy,which is firstly created by Wall Street trader Jesse Livermore.With the rapid development of computer technology,Pair trading is more and more widely used in the financial markets.Since March 2010,the securities market in our country have carried out margin trading and stock index futures business,which provided the premise and foundation for the pair trading strategy in the implementation of the securities market in our country.there are two major classes in the current study of pairs trading.The first is the one that focus on statistics and data mining method to realize pair trading.The other is the one that focus on equation method to realize pair trading.One of the first kind of research is more widely used in application,but it has a mainly imperfection that it is unable to control risk by determing the number of the pair underlying.In this paper,we use the sencond one which is focus on equation method to study the optimal strategy on the condition,which pair spread meet the O-U process.Unlike previously some scholars research content,we consider stoping loss and checking surplus stratrgies in this paper.In the third section,we established HJB equation which satisfy the optimal control.But this equation is diffcult to find the analytic solutions.So we use the finite difference method to detemine the numerical solution of the HJB equation.In order to keep the matrix positive semidefinite,we use wide stencil method to establish the HJB equation's numerical scheme,so that we established a nolinear algebraic equations which is approximate to the HJB equation.After that we use iteration method and PCG method to the algebraic equations.Then we make a numerical analysis.In the forth section,we prove the consitent,the monotonivity,the stable,the convergence of the scheme and the iteration method that has been established in the third section.In the fifth secton,we further expanded the model of the optimal strategy which is based on pair trading.We use the mean variance model as the aim of investors.Also considering stop check and surplus check strategy,we established the HJB equation and uesed method which was applied in the third section to solve the numerical solution of the equation.In the end,we maked a numerical analysis.We compared the optimal strategy of the third chapter and the fifth chapter of the differences as the other parameters were the same.