Statistical Study of Adjusting Mortality Tables Problems for Modelling the Reserves of a Life Insurance Company

Life insurance companies take into account many factors when calculating mortality tables and modeling insurance reserves. The problem is that when an insurance portfolio consists of a relatively small number of policies, the application of the mortality table becomes more difficult. The purpose of the work is to determine how the adjustment of mortality tables for a small portfolio will change the calculated reserves for a life insurance company. Research objectives: 1) To study the existing literature on the adjustment of mortality tables and calculation of insurance reserves. 2) Select data on life insurance portfolios in various insurance companies. 3) Adjust mortality tables in several ways using stochastic and parametric models. 4) Simulate insurance reserves using the results of adjusting mortality tables and various actuarial methods. The methodological basis of the study consists of primary methods of data processing and analysis, stochastic models (Lee-Carter, Plat, RH, APC), parametric models (Gompertz-Makeham), similarity measures (QDEV, ERL, A/E), verification of statistical hypotheses, actuarial methods for calculating insurance reserves, etc. methods and various statistical tests. According to the results of the work, the following hypotheses were confirmed: the first hypothesis about the effectiveness of stochastic and parametric models for constructing mortality tables on a small sample was confirmed, since we got several high-quality models with good indicators. The second hypothesis about the identification of significant differences between the modified mortality tables and the original ones was also confirmed, since similarity measures showed the relevance of replacing some historical tables with modified ones. The third hypothesis that the new insurance reserves are much closer to the real mortality statistics for the portfolio was also confirmed for several models (in particular, the age-cohort-period and Lee-Carter models). The best strategy for an actuary of a small insurance company according to the results of the study: 1) Mandatory calibration of data for each age range, since all models show themselves differently at different age ranges. 2) Comparing the quality of each of the models using classical tests for normality and standardization of the distribution of residues, as well as a Chi-square test showing how much the modeled data differs from the historical ones. 3) Using similarity measures to determine whether it makes sense to replace historical mortality tables with modified ones. 4) Choosing the best mortality table as a combination of different models for each age range. 5) Calculation of reserves for data in which insured events have already occurred and assessment of the degree of their modification.