Modeling of pension income and expenditures based on the Verhulst equation and polynomial regression with demographic projections

Abstract

To calculate the demographic load factor in this work, the forecasting of the working-age population of Russia was carried using the polynomial regression equation of the fourth degree with an accuracy of 0.227% and forecasting the number of people older than working age using the Verhulst equation (prediction accuracy of 1.084%) for the period from 2023 to 2031 (9 years). An economic and mathematical model was developed for calculating pension income and expenses for the implementation of individual (personalized) pension accounts of citizens and a stress analysis of the model was carried out based on an assessment of the impact of the pension contribution rate, average monthly salary, average investment income rate for transactions with pension funds of citizens (rate of return) and growth rates salaries, ensuring a balance between pension income and pension expenses of citizens. The practical implementation of the developed economic and mathematical model shows that the minimum value of the rate of return, ensuring balance between pension income and pension expenses of citizens, is 1.408%. The minimum average monthly salary is 22,949.39 rubles; the contribution rate to the Pension fund is estimated at 18.813%.