Optimal Investment Strategies For Market Models With Reversal And Momentum

In this paper,the optimal control problem for stochastic differential equations with time-delay market model is studied.The dynamic market model investigated in this paper combines two phenomena related to market price trend in the actual situation: reversal and momentum,and portrays them in the drift term of the system.By using the stochastic maximum principle of the control system with time-delay,the optimal investment strategy is deduced and the formal solution of the problem is obtained.In this paper,two utility functions are considered: the CRRA utility function and the exponential utility function,and the respective optimal solutions are obtained respectively,and the theorem results are proved in two chapters.The purpose of this paper is to solve the problem of stochastic optimal portfolio solution of a dynamic model with time-delay control system,and the main achievement is to obtain the formal solution under two utility functions.See the Lemmas and the proof part of this paper.The significance of this paper is that the stochastic differential control system with time delay is different from the Markov situation,which makes the dynamic programming principle not applicable.Therefore,the idea of this paper is to derive the optimal solution of the control system by using the stochastic maximum principle.The results obtained in this paper are to supplement the optimal solution expression of two utility functions and its reasoning proof on the basis of the original work,and the expression of two solutions presents a certain consistency.