Optimal Investment Strategy Of DC Pension Plans Based On Two Types Of Administrative Charges Under CIR Model

With the increasing trend of population aging around the world,the defined contribution type(DC-type)pension plan has gradually become the pillar of the aged security system.In most DC pension plans,managers will charge administrative charges to the insured,which has a significant impact on the optimal investment strategy and terminal wealth of the pension.For the above reasons,this thesis studies the optimal investment strategy of DC pensions and the equivalent administrative charges when administrative charges exist.This thesis assumes that the term structure of interest rates obeys the CIR model,and DC pension funds can be invested in financial markets that contain risk-free assets,zero-coupon bonds and stocks.Pension managers charge administrative charges in two ways: charge on balance and charge on flow,with the aim of maximizing the expected utility of the member's terminal wealth.The dynamic programming principle is applied to obtain the HJB equation that the corresponding value function satisfies,and the variable separation method,Legendre transformation and duality theory are used to solve the explicit solution of the optimal investment strategy under CRRA,CARA and the more generalized HARA utility.At the same time,based on the theory of certainty equivalent,this thesis compares the terminal certainty equivalent wealth under the two charging methods,and finds a balance between the two charging methods,namely equivalent administrative charges.This thesis also conducts a numerical simulation based on the results of theoretical derivation,discusses the influence of the main parameters on the optimal investment strategy under the two charging modes,as well as the sensitivity of terminal deterministic equivalent wealth to administrative charges,and conducts calculations on equivalent administrative charges.According to the results of numerical simulation,the explanation of the corresponding economic meaning is obtained.The conclusions of the study are:(1)The investment accumulation period,administrative charge rate,interest rate risk and risk aversion coefficient have greatly affected the optimal investment strategy of DC pensions;(2)The charge of administrative charges will reduce the terminal certainty equivalent wealth;(3)When the member has CRRA utility,the risk aversion is lower,Terminal deterministic equivalent wealth is more sensitive to changes in administrative charges rates;(4)Equivalent administrative charges are only related to risk-free interest rates,accumulated time,and charge rate parameters based on flow;(5)Equivalent administrative charges increases strictly with the age of the member.Based on Luis(2016)and Fangchao Li et al.(2019),this thesis adds zero-coupon bonds to the financial market,and takes into account the impact of interest rate risk,making our model more realistic and guiding the research conclusions more practical and instructive,promoting the relevant research conclusions of the above-mentioned literature.