Delegated Portfolio Management Problem Under Co-integration Model

In the field of delegated portfolio management,when the investment field of the agent is limited to a specific industry and the risk asset price satisfies the co-integration relationship,what factors will afect the optimal cont.ract and the optimal portfolio.This problem is worth researching.This thesis starts from the classical model of delegated portfolio man-agement,combining with the theory of matching transaction based on co-integration model,and uses the linear contract commonly used in the industry to establish the mathematical model.Through the method of stochastic con-trol,the HJB equations of the principal and agent optimization problems are obtained,and the method of dimension reduction is used to solve it.Finally,the optimal strategy and optimal contract of the delegated portfolio manage-ment problem under the co-integration model are obtained.Through simu-lation and comparative analysis,it is found that the optimal policy obtained is more profitable than the optimal policy obtained by using the geometric Brownian motion model.At the same time,it is founded that the factors for example the reservation utility of the agent,the capital scale invested by the initial client,the initial co-integration relationship and the Ratio of risk aversion coefficient of principal and agent have impact on the the optimal con-tract.The optimal strategy is affected by time t,co integration vector zt,and a coefficient related to the risk aversion level of principal and agent.Basing on the results of the model and simulation,it is suggested that investors should choose hedge fund or limit the investment scope of agent before investment,which is conducive to improve the interest of investors.At the beginning of investment,they should have a certain understanding of the co-integration relationship within the industry,and improve the initial investment scale,which can effectively reduce the investment cost.