Mean-Variance Model For DC Pension Plan Under Stochastic Environment

The pension insurance system is an important means to promote the development strategy of aging in China,and its purpose is to optimize the distribution of social resources,to ensure that pensioners can get a stable and reliable source of income after retirement,and to meet the basic needs of life.It makes a great contribution to the harmony and stability of the society.In addition,due to the slowdown of China’s economic development,interest rates are decreasing and many private institutions are not earning as much in the stock market,so people are focusing on the pension market to maintain their quality of life after retirement and to enhance their sense of access,happiness and security.In order to explore the potential of the aging society and to stimulate its vitality,the academic debate on pensions has become a focal point.At the same time,the most important concern in pension plans is the maximization of returns.It can be said that the asset allocation of pensions in the financial market and whether they can achieve the goal of preserving and increasing their value are related to whether the quality of life of each pension holder can be guaranteed after retirement,as well as to the overall development of the country,the well-being of hundreds of millions of people and the harmony and stability of society.Firstly,in real life,the level of salary and the price level of stocks are often not immutable.In order to get closer to the reality,considering stochastic interest rates and stochastic salary,we consider it under the Hull-White interest rate model,and the pension can be invested in a risk-free asset and a risky asset.In order to achieve the expected goals of plan holders,we research the optimal investment problem of DC pensions with the mean-variance as the goal.Using the principle of stochastic dynamic programming,the HJB equation of the optimal investment is established.Through Legendre transform and duality theory,the explicit solution of the efficient strategy and frontier is obtained.Lastly,through the numerical analysis of the obtained results,the corresponding Economics explained.Secondly,considering the impact of inflation in real life,we invest the pension in a risk-free asset,a risky asset and an inflation index bond.In order to achieve the expected goal of plan holders,we study the optimal investment problem of DC pension with the mean variance as the target,and establish the corresponding HJB equation according to the principle of stochastic dynamic programming.By using Lagrange transformation and duality theory,the explicit solutions of effective investment strategy and effective boundary are obtained.Finally,through the numerical analysis of the obtained results,the corresponding Economics explained.