| Pension is a very important part of the national social security system,and the research on pension is an enduring research topic.In contemporary society,how to preserve and increase the value of pension become hot issues.One of the methods to preserve and increase the value of pension is to abandon a single investment and turn into multi-channels of investments,including risk-free assets(such as bonds,investment funds)and risk assets(such as stocks,derivatives)investment.Therefore,it refers to the investment proportion of the risk-free asset and risk asset.No matter how to arrange investment portfolio of the pension insurance fund,we are on the basis of security to maximize profit or minimize the risk of investment.In this paper,we mainly study the stochastic optimal strategy of CEV Model in DC pension portfolio.In order to minimize terminal wealth variance under pre-given terminal wealth expectation,we take the Mean-Variance as the target.Through the transformation of the utility function,the objective function is transformed into the extreme value problem of the Mean-Variance utility function.By using stochastic optimal control theory,we establish the HJB equation of pension optimal investment and calculate the explicit solution for the Mean-Variance utility functions and then we also obtain the optimal strategies for the pension portfolio before and after the retirement.Finally,we use numerical simulation to illustrate the optimal strategy to help DC type pension investors to establish optimal portfolio. |
