Continuous Mean - Variance Portfolio Problem Is Studied with Time Delay Using Stochastic LQ Control Theory

摘要

The mean - variance portfolio selection model based on the expectation and variance of return on assets to measure the expected return and risk of investment. Due to the financial sector complicated variety of events, each financial problems from changes to know its essence, the change rule, from the change of strategy to formulate relevant policy and policy into effect, etc, the process inevitably has a certain lag. Therefore, in order to better reflect the actual situation, we study the portfolio model with delays in this paper. By joining our delay control item, the optimization model was established, the goal is to maximize earnings expectations. In this paper, it studies the continuous time without delay the mean - variance portfolio problems on the basis of existing research. It established auxiliary problem using the stochastic linear quadratic optimal control theory. Using the maximum principle, the solution of the optimal investment strategy are given and it analysis the case, the conclusion is in conformity with the actual. It studies the existing time delay portfolio strategy problem in discrete time case. Based on the stochastic LQ optimal control theory, it established the discrete mean - variance time model with time delay. The paper has carried on the solution and example analysis. And according to the maximum principle, the optimal control model of the general form of the input delay stochastic LQ problem are obtained. The final result shows that when the delay is zero, the results is the same as the model without time delay.