Research On Optimal Investment Consumption In Different Time Domain

As a basic problem in the financial field,the optimal investment consumption problem has been paid much attention by scholars both at domestic and abroad.The optimal investment and consumption problem is mainly to study how to in-vest in various assets while making consumption,to maximize the total utility of consumption and final wealth.On the basis of Merton's research on the optimal investment consumption,the assumptions are relaxed in this paper.Based on two different time domains and three representative consumption utility functions,the optimal investment and consumption strategy is studied.By solving the different models,how the parameters affect the optimal investment and consumption strat-egy in different market environment can be analyzed and compared.And then,a scientific theoretical basis can be provided for investors to invest and consume effectively.According to the diversity and uncertainty of the real financial market,this paper mainly carries out the following three aspects:First,a continuous time portfolio selection model is established,and the HJB equation satisfying the value function is solved by using the dynamic programming principle,and the general solution of continuous time optimal investment and con-sumption problem is obtained.Second,under the continuous time portfolio model,the analytic expression of the optimal investment consumption problem for different utility functions in different time domain is given respectively.Third,the optimal investment consumption model under different utility func-tions is simulated,and the influence of the parameter variables on the optimal investment consumption strategy is combined with the graphic analysis.The following is a brief introduction to the contents of each chapter:Chapter 1 summarizes some related background of investment consumption problem and the innovation and structure of this dissertation.Chapter 2 briefly introduces the financial market model and the preparatory knowledge related to this article.Chapter 3 mainly studies the continuous time portfolio model.First,we assume that there is a risk-free asset and a kind of securities on the market,assuming that the share of the secondary securities is a random process.A continuous time portfolio selection model is established to maximize the cumulative mathematical expectation of consumption and final wealth utility.The HJB equation of the value function is obtained by using the principle of dynamic programming.And the general solution of the optimal investment portfolio is obtained.As a result,all rational investors in the stock market have the same optimal portfolio,independent of the specific utility function form.Chapter 4 gives the solution of different investment consumption models.For the three different utility functions,the optimal investment consumption model in the infinite time domain is solved,and then the solution of the model in the finite time domain is calculated.Chapter 5 is the numerical simulation of the optimal investment consumption strategy of each utility function.