Study On Optimal Investment Problem For DC Pension Plan With Stochastic Volatility And Inflation

With the progressive development of medical level, the whole world will be confronted with a serious problem of aging population. The issue of old-aged security is closely related to the social stability and economic development of a country. Thus, the pension problem becomes an important part of government’s reform. The study on the issue of attaching great importance to the optimal investment on pension can not only realize the maintenance and appreciation of the pension, but also have practical significance on aging population of the whole society. As a result, many scholars have considered the pension management as an important research content of actuarial science and financial mathematics. However, in reality it takes a long time to invest pension with various risks which will cause the change of investment income. Therefore, we first bring inflation and stochastic interest rate into the investment model of pension. Then, for countless empirical studies have suggested that the earnings of risk assets (stock) and variance is random, under which we further study the effect of inflation on pension investments.This article is mainly aimed at studying Defined-Contribution (DC) pension, analyzing the stochastic interest rate, the effect on the investments of DC pension of inflation and random fluctuations. Firstly, we introduces inflation factor under the framework of stochastic interest rate, in which the stochastic interest rate is depicted base on the vasicek model and inflation obeys reversion process. Secondly, by using the theory of stochastic control, the corresponding HJB equation is obtained. Then, in the case of power utility function, the explicit solution of optimization value function is obtained. Finally, by fixing some parameters, the effect of investment of time and volatility of inflation on pension investment strategy is analyzed.On the other hand, this paper studies the optimal investment problem of DC pension under the combined influence of inflation factor and random fluctuation. And by using the dynamic programming principle, this paper gains explicit solution of optimization problem. We also discusse the instantaneous volatility, inflation volatility, the level of Pension wealth and risk aversion coefficient have influence on pension investment strategy. The numerical analysis results show that when there is a positive correlation between the risk asset and inflation, with the increase of inflation volatility, investors will be more cautious to reduce investments in risky assets. When there is a negative correlation, investors will be radical to believe that the greater the risk, the higher the income, so that they will increase investments. We can also get a conclusion that the higher the wealth of the pension level, the lower the proportion of risky assets investment.