Study On Mean-Variance Portfolio Selection With Time Delay

Mean-variance portfolio selection model use the mean and variance of re-turn on assets to measure the expected return and risk of investment. Today’s financial world is very complicated, and the international financial situation is changing rapidly. When the economic situation changes, we need time to recognize the need of changing strategy and then formulate relevant strate-gy, when the strategy goes into effect, there is a certain lag inevitably in the process. Therefore, in order to make the model reflect the actual situation better, we study portfolio model with time delay, with the aim of optimizing the existing model and maximizing the expected revenue.In this paper, based on the mean-variance model without delay, we stud-ied the model with time delay by using the the latest result of "LQ optimal control problem with input time delay". We studied the model of discrete and continuous condition respectively. Through the establishment of model, we present the optimal investment decisions and carry out some analysis.The main contents and results are listed as follows in the order of chapters:1. Based on the previous research, through establishing auxiliary problem, we study the continuous time mean-variance portfolio problem without time delay by using the stochastic linear quadratic optimal control theory. With the help of maximum principle, we give the explicit solution of the optimal investment strategy, and the detailed solving process is given. In the premise of a given expected return, we can calculate the percentage of investing in risky assets through the above method, which have a guiding role. In addition, we use an example to demonstrate the effectiveness of the model, and get conclusions corresponding to actual situation.2. We study the discrete time portfolio strategy problems with time delay. Based on the stochastic LQ optimal control theory, a discrete model with time delay is established, and then solve the model. According to the maximum principle, we obtain the optimal investment strategy through the recursive method. We get conclusion that when investors consider delay, they deter-mine strategy on the basis of the current state and the income generated from previous strategy sequence. Considering the time delay factors conform to the reality better.3. We build continuous time mean-variance model with time delay, and according to the maximum principle, we get the solution of general stochastic LQ optimal control problem with time delay. Then according to the results, we obtain the optimal investment strategy of the model. We get the conclusion that the model without time delay is a special case of the extended model with time delay.The main innovations of the article are as follows:obtain analytic solution of the general LQ stochastic control problem with time delay. On the other hand, broaden the depth of the the mean-variance problem by adding time-delay factors, and optimize the original model. The result is closer to the reality.