DC-type Pension With Minimum Income Guarantee In A Random Environment

Pension system is to provide pensions for the social members of social system,there are two main kinds of pension fund,the defined benefit pension plan(DB)and the defined contribution pension plan(DC).In the DB pension plan,the benefit at retirement is fixed in advance and the contribution rate from the pension plan participation is important to ensure the plan's balance.Related financial risk borne by the fund manager in the DB pension plan.In the DC pension plan,the contribution rate is fixed in advance and the benefit depend on the return on investment of pension.Related financial risk borne by the pension plan participants in the DC pension plan.Because of the population evolution and the development of capital market,DC pension plan become play a more and more important role in the social security system.Due to the DC pension plan leaves the plan member facing the risks from the market and does not guarantee benefit in the future.So the DC pension plans with minimum guarantee are attractable.It is very necessary to concern the optimal investment strategy of pension plan in a stochastic rate and the stochastic volatility.According to the current situation of financial markets,investors can put money to invest in zero-coupon bonds,riskfree assets and stock.This paper studies DC pension fund with minimum guarantee in a stochastic affine interest rate and stochastic volatility framework.First,in the first chapter introduces the DC pension financial markets and the main research status of the optimal investment strategy problem.The second chapter prepared in this paper,the basic knowledge.In the third chapter,first,by using dynamic programming theory,we obtain the closed-form solutions to the optimal investment strategies for exponential utility;Next,by applying the Legendre transform and duality theory,we obtain the closed-form solutions to the optimal investment strategies for logarithm utility,and a numerical example is given respectively analyzes the market parameters respectively under the exponential utility and logarithm utility function for the optimal investment strategy.The fourth chapter gives the conclusion and prospect of the paper,the deficiencies,and the direction of the future research.