Research On Actuarial Model Of Pension Account Payment Rate Under Stochastic Interest Rate

With the change of population structure,the birth rate and mortality rate of our country are changing from high to low in recent years,which results in the aging of the population and the increasing of this phenomenon,plus the implementation of the transition of the endowment insurance system.The state needs to support the former "The elderly" unpaid pension population,resulting in a certain amount of debt,and the " The youth" generation has to pay not only for their own generation,but also to make up for the government’s liabilities in the pension gap."Young people" and the government are overburdened.Therefore,this paper considers the important factors that the economic market interest rate can affect the pension income.By constructing the actuarial model of pension income balance,this paper deduces the expression of pension individual account contribution rate under random interest rate.The combined stochastic process is introduced to improve the model,and the agreed contribution rate of personal account is calculated by using mathematical software as a tool.Empirical studies show that interest rates have the most significant impact on individual account payment rates.It is also found that wage growth,retirement age,retirement gender differences and other factors should not be ignored.The specific work of this paper as follows:Firstly,on the basis of reading the relevant literatures at home and abroad,this paper defines the concepts of interest and interest force,interest rate and discount rate,final value and present value;It introduces the relationship between the basic survival model and the survival function,gives the probability of survival under different gender conditions,and then summarizes the three aspects of the pension insurance system,including the concept,the model and the historical process.The above related theories provide theoretical support for the subsequent research.Secondly,the actuarial model of individual account payment rate under fixed interest rate is studied.From the point of view that the pension paid by the insured person during the retirement payment period is equal to the increase in investment savings paid during the work contribution period,an actuarial model of the individual account contribution rate is constructed,based on the perspective of gender differences.By simulating the value of pension personal account contribution rate under fixed interest rate,it is found that the actuarial model of personal account contribution rate under fixed interest rate has its limitations.It is necessary to consider the characteristics of random change of interest rate in the real financial market.It is also necessary to establish an actuarial model of individual account payment rates at random interest rates.Finally,the actuarial model of individual account contribution rate under random interest rate is studied.The interest rate is randomized,and the random interest rate model is constructed by using the Brownian motion,the reflection Brownian motion,the Gauss process and the Poisson process respectively.Based on different stochastic interest rate models several expressions of pension personal account contribution rate are obtained.This paper focuses on the joint model of Brownian motion and Poisson process.The model takes full account of the effect of information of different properties on interest rate,and analyzes the influence of each parameter change on the model by means of mathematical software.The empirical results show that market interest rates have the most significant impact on pension individual account contribution rates.In addition to retirement age,gender differences and wage growth rates will also have an impact on pension individual account contribution rates.Many factors should be taken into account in the formulation of the old-age insurance policy.The conclusion of the study accords with the actual situation of the pension and has reference value for promoting the reform of the old-age insurance system.