Application of probabilistic and stochastic models and data mining for forecasting the contingent of old age pension recipients in the context of systemic uncertainty

The object of the research is mathematical models for forecasting the contingent of pension recipients in conditions of uncertainty caused by both the reform of the pension system and the impact of armed aggression. Based on the study of statistical information on the structure and dynamics of the contingent of pensionrecipients, an approach to uncovering systemic uncertainty in the task of forecasting the contingent of pensioners is proposed. This work is part of a study of the application of data mining methods of intellectual data analysis and mathematical modeling in information technology intended for use in the pension system. The main focus of this work is on forecasting the dynamics of the contingent of pension recipients by age, in particular, forecasting the number of newly appointed pensions. The difficulty of forecasting the contingent of pension recipients, in particular by age, is connected with the fact that it is necessary to ensure the representativeness and variability of data sets. In addition, it should be taken into account that a significant number of factors must be included in the model in accordance with the requirements of regulatory documents. Another problematic issue is that the time series of the investigated indicators, such as data on the insurance experience of insured persons (based on the results of a sample survey), may contain significant (more than 40 %) gaps that can be filled only on the basis of primary (paper) documents. Therefore, the input data sets are formed with assumptions about the probability of the accumulation of insurance experience in various groups of insured persons. The paper proposes an analytical toolkit based on the use of probabilistic and statistical models in the form of Bayesian networks, intended for use in specialized decision-making support systems of the Ukrainian pension system. In the course of the study, a number of numerical experiments were carried out, in which the correctness of the proposed method was investigated. The proposals presented in the paper will improve the stability of the pension system of Ukraine, including through a more accurate definition of the dynamics of the contingent of pension recipients and, accordingly, the costs of pension payments. The proposed models and methods can be used as part of decision-making support systems of state and public administration bodies to analyze the results of reforming the pension system.