Research On The Actuarial Model Of 'Recessive' Replacement Rate Of The New Rural Social Pension Insurance Under Rural Land Circulation System

With the rapid economic development in China,the improvement of the gross national product has led to the people's quality of life and their average life expectancy has been continuously extended.From 1950 to 1970,the average fertility rate in China reached 6.11(fertility rate dropped to 1.22 in 2000).Those born in that era were gradually entering old age,which made the problems of population aging and elderly dependency ratio more and more serious in our country.In recent years,due to the rapid economic development in cities and towns and the reduction of food prices,most rural laborers choose to work in cities and give up their cultivated land,resulting in a serious reduction in the utilization rate of cultivated land and even the abandonment of cultivated land.Although the new-type rural social endowment insurance system established in China has some improvements over the traditional rural social endowment insurance system in 2009,the new-type rural social endowment insurance system has some problems such as the protection level and the small coverage area.Based on the national conditions of our country and actuarial theory,this paper studies the "recessive" replacement rate of the new rural social pension insurance under the joint stochastic interest rate.Specific work as follows:Firstly,on the basis of the target replacement rate of new-type rural social pension insurance under the fixed interest rate,and combining with the land circulation system,taking into account the per capital cultivated land area and the investment cost of agriculture,this paper constructs a new type of rural social endowment insurance Actuarial model of "recessive" substitution rate.Through the analysis and comparison of the value of new rural social old-age insurance replacement rate,it is concluded that the choice of payment grade,the starting payment age and the fund annual interest rate have a significant impact on the replacement rate.Explain the advantages of the "recessive" replacement rate of new rural social endowment insurance over the original target replacement rate.Second,taking into account real-world interest rates is subject to many factors that are constantly changing.In this chapter,we combine the interest rate using Gauss and Poisson processes,and the reflection Brownian motion and Poisson process.To establish the actuarial model of the target replacement rate of the new rural social endowment insurance under therandom interest rate and the actuarial model of the "recessive" replacement rate of the new rural social endowment insurance under the random interest rate.The expectation value of the replacement rate of the new rural social endowment insurance and the expectation value of the "recessive" replacement rate of the new rural social endowment insurance are deduced.Finally,Monte Carlo simulation algorithm and the use of MATLAB programming to simulate the above model,draw the conclusion that the new rural social endowment insurance substitution rate empirical function distribution graph and empirical function density graph under the combined model of Gauss,Reflex Brownian motion and Poisson process respectively.Comparing and analyzing the "recessive" replacement rate of the new rural social endowment insurance and the original target replacement rate,come to the new rural social endowment insurance "recessive" replacement rate can reach the pension insurance "maintain the basic" principle.The above simulation results provide theoretical support for relevant departments to strengthen research and development of the new system of agricultural insurance reform.