Research On The Optimal Investment Strategy Of DC Pension Considering Management Cost And Mispricing

With the aging of China's population structure,the issue of optimal investment strategies for pensions has become increasingly important.It is mainly because DCtype pensions make managers and insurers together share risks and benefits,which is in line with social development,that DC-type pensions have gradually replaced the original DB-type one.This paper focuses on the optimal investment strategy of DC-type pensions in consideration of transaction costs and mispricing,using a stochastic optimal control model to find its explicit solution and numerically analyze the results.The main results obtained in this article are as follows:First,the optimal investment strategy of DC-type pensions considering random wages and management costs under the CEV process is studied.Assuming that the financial market consists of risk-free assets(bank deposits)and risk assets(stocks),of which risk assets obey the CEV process,and the factors of random salary as well as management cost are added to the model.In this paper,the maximum expectation of wealth at the moment of retirement is targeted.Firstly,the dynamic programming principle is used to obtain the HJB equation of the optimal investment strategy,followed by the logarithmic utility function.Next,Legendre transformation is used to solve its explicit solution.Finally,the strategy is numerically simulated to analyze the impact of management cost,pension management period,constant elasticity coefficient ? in the CEV process,wage levels,wage fluctuations,stock fluctuations,and contribution rate on optimal investment strategy.Second,we have studied the optimal investment strategy of DC-type pensions considering mispricing.Assuming that the financial market consists of three parts:risk-free assets(bank deposits),market indexes,and a pair of stocks with mispricing.Among them,the market index and the stock obey the geometric Brownian motion model,and through the wrongly priced stock price process,a wrongly priced stochastic differential equation is constructed.Under the aim of maximizing the expectation of wealth at the time of retirement,the dynamic programming principle is firstly used to obtain the HJB equation of the optimal investment strategy.Secondly,in the case of the CRRA utility function,the explicit solution is solved by guessing the function form of CRRA utility.The strategy is then numerically simulated,and the effects of mispricing,wealth level,and investment duration on the optimal investment strategy are analyzed.Based on the above two points of work,this paper draws the following conclusions: Under the CEV model,as management costs increase,the proportion of investment in risk assets will decrease;the higher the salary level of pensioners,the greater the risk assets will increase.Compared with the stock's own fluctuations,the fluctuation of wage levels will be far greater than the impact of stock fluctuations on the investment decisions of pensioners.Once the wage level fluctuates rapidly,there will be more to invest in risk-free assets instead of reducing the proportion of investment in risky assets.When considering the model of mispricing,when the same stock with the mispricing phenomenon has the same liquidity,the optimal investment decision of the DC-type pension manager is to choose to buy the undervalued stock and to sell the corresponding equivalent amount.When the liquidity is different,the proportion of investment in stocks with better liquidity will be increased;and when pensioners have a longer retirement period,more funds will be invested in mispriced assets,in which stocks have stronger anti-risk capabilities.The closer to the retirement time,the investment in such stocks will gradually decrease,and more funds will be invested in risk-free assets and market indexes.