The Mathematical Model And Simulation Analysis Of Income And Expenditure Projections Of The Pension Insurance Fund For Urban Workers

Implicated by the aging of population,the pension funds of urban workers become obviously unsustainable.As a result,burden keeps rising continuously.The budget of National Social Insurance Fund shows that in 2015,the gap has already reached 300 billion.In this paper,we construct a systematic dynamic model of pension funds by analyzing the elements that control the operation of pension funds.History data is used to prove that our model is correctly built.Then we propose a schema of reforming the operation of pension funds and simulate it by using our model.The main focuses and innovations of this paper are summarized as follows:(1)Firstly,we introduce research about endowment insurance at home and abroad,analyze the advantages of the system dynamics model with respect to the traditional actuarial science in the simulation of the fund operation,and point out the problems existing in the research of the present stage: using the population life table method to calculate the insured population leads to tremendous deviation,analysis on the impact of financial subsidies on the fund is not accurate enough,the accuracy of simulation results is not high.(2)Then,we introduce the theory and process of the system dynamics modeling,and describe the application of math in such model,current situation of pension insurance in our country is also analyzed as well as related problems.(3)Our fund model composes of three parts: population system,economic system and the endowment insurance system.Considering the influence of the national birth policy on fertility rate and the changing trend of sex-specific and age-specific mortality,we propose to replace the traditional population life table method with an aging high-end chain model in the population system,which makes the result better.Taking the effects of economic development and inflation into account,we associate the average wage and per capital pension with the level of GDP in the economic system.In the fund system,we introduce the financial subsidy controlled by the national financial expenditure.By comparing the financial subsidy level of China and western countries,we conclude that there is still some space for improving financial subsidy of our country.To ensure the rationality and accuracy of our model in simulating the operation of endowment insurance,we use SPSS software to carry out the numerical fitting in the statistical measurement of related variables.(4)We construct the system dynamics model of endowment insurance fund according to the numerical analysis of relevant variables,based on which we simulate the operation of endowment insurance fund from 2010 to 2045 via the model.By comparing the simulation results with the historical data,we prove that the simulation based on our model has reached the expected effect,since the relative error are less than 3.5%.On the basis of the model,we discuss the reform strategy of the sustainable operation of the pension fund by simulating the situation of the gradual delay retirement plan,the fund into the market plan and other related policies on the fund operation,finally put forward the reform suggestions.