No abstract

1 A number of models for generating statistical data in various fields of insurance, including life insurance, pensions, and general insurance have been considered. It is shown that the insurance statistics data, as a rule, are truncated and censored, and often multivariate. We propose a non-parametric estimation of the distribution function for multivariate truncated-censored data in the form of a quasi-empirical distribution and a simple iterative algorithm for its construction. To check the accuracy of the proposed evaluation of the distribution function for truncated-censored data, simulation studies have been conducted, which showed its high efficiency. The proposed estimates have been tested for many years by the IAAC Group of Companies in the actuarial valuation of corporate social liabilities according to IAS 19 Employee Benefits. Apart from insurance, some results of the work can be used, for example in medicine, biology, demography, mathematical theory of reliability, etc.

The aim of the paper is to develop new statistical indicators that can more accurately characterize the situation on the labor market, based on the available operational and accessible statistical information. The object of this study is statistical indicators characterizing the complete duration of general unemployment. The empirical basis of the study was the data of the Sample Labor Force Survey (LFS) for 2017–2020. The research methodology consisted of a logical analysis, transformation and calibration of the initial statistical data (statistical methods of survival analysis were used for their processing, including regression analysis of censored data), as well as an analysis of specialized scientific literature and internet sources. As a result of the study, a procedure was developed for estimating the indicators of the complete duration of unemployment according to the data of the one-time sample survey of unemployed citizens, which involves the use of statistical methods for analyzing survival, transformation and calibration of the initial statistical information. Stochastic modeling has shown the high efficiency of the proposed procedure. The authors conclude that the practical examples given in the article for calculating the distribution function of the complete duration of unemployment according to the LFS data for 2017–2020 and derived statistical indicators, including its median depending on the age, sex and place of residence of unemployed citizens, as well as other research materials can be used by Rosstat, federal and regional executive authorities responsible for the organization and operation of social protection of the unemployed, in research and evaluation of the labor market and labor relations.

На основе разработанной имитационной модели российской системы социальной защиты безработных исследуется влияние экономического кризиса, вызванного пандемией COVID-19, демографических процессов и повышения пенсионного возраста на расходы федерального бюджета на выплату пособий по безработице. Проанализированы тенденции общей и зарегистрированной безработицы различных социально-демографических групп в 1992-2020 гг. Особое внимание уделяется периодам экономического спада и восстановления. На основе выявленных закономерностей разработаны сценарии моделирования. Расчеты показали, что бюджетные расходы на выплату пособий по безработице при неблагоприятном сценарии возрастут многократно. В качестве возможного решения проблемы предлагается перевод системы социальной защиты безработных на страховые принципы. Определены временные рамки, в которых реформа системы будет менее затратна для федерального бюджета.

The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including policies with deductible) and claims incurred. Real data of some Russian insurance companies on non-life insurance contracts illustrate some opportunities of the proposed approach. The point and interval estimates of net premium, claims frequency, claims reserves including IBNR and OCR, are thus obtained. The resulting estimate of claims reserves falls in the range of reasonable estimates calculated on the basis of traditional reserving methods (the chain-ladder method, the frequency-severity method and the Bornhuetter-Ferguson method).The proposed methodology is based on additive estimates of a company's financial indicators, in the sense that they are calculated as a sum of estimates built separately for each element of the sample (claim). This allows using the proposed methodology to model insurance companies' financial flows and, in particular, to solve the problems of reserve redistribution between particular segments of insurance portfolio and/or time intervals; to adjust risk as part of financial reporting under IAS 17 Insurance Contracts; and to deal with many other tasks.