Abstract
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 (linear quadratic) optimal control theory, it established the discrete time model with time delay. The paper has carried on the solution and example analysis.
Highlights
In today's capital market, the pursuit of profit maximization is the main intrinsic motivation of each investor, but investment is risky, the returns and risk of venture capital is a problem of two aspects, along with investment of high yield and a corresponding must be high risk
Portfolio theory in the first time, it provides a method to solve the problem of single stage investment Portfolio, the prototype of the mean - variance model
On the basis of existing research, this paper presents continuous time mean-variance model without time delay, through establishing of auxiliary problem, the original problem is transformed into LQ control problem, and use stochastic LQ optimal control method to get the analytic solution of the optimal portfolio strategy
Summary
In today's capital market, the pursuit of profit maximization is the main intrinsic motivation of each investor, but investment is risky, the returns and risk of venture capital is a problem of two aspects, along with investment of high yield and a corresponding must be high risk. Guo [19] studies the investment decision making problems in the random market parameters, respectively, considering the stock prices have two kinds of situations of jumped and continuous, using the stochastic LQ optimal control and backward stochastic differential equation method, getting the analytical form of effective investment strategies and efficient frontiers. Lim [20] studies the mean - variance optimal combination problem In case of not allow short-selling; for the continuous-time portfolio selection optimization problem in the case of liabilities, C. On the basis of existing research, this paper presents continuous time mean-variance model without time delay, through establishing of auxiliary problem, the original problem is transformed into LQ control problem, and use stochastic LQ optimal control method to get the analytic solution of the optimal portfolio strategy. According to multi-phase mean-variance portfolio model, established discrete time variance model with time-delay, gave the solution of general form discrete LQ optimal control problem with time delay, analyzed of the example
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