Risk Evaluation Using the Theory of Generalized Actuarial Calculations

The article is prepared based on the results of theoretical studies conducted by the authors in the field of actuarial calculations, the improvement of which is one of the development directions for statistical science.

In modern economic conditions, the assessment of risks inherent in economic entities in all spheres of activity and leading to significant losses, such as credit, operational risk, liquidity risk, and so forth is of particular importance. Quantitative assessment of the level of risks is the subject of actuarial calculations. However, the existing apparatus of actuarial science is mainly focused on solving specific issues facing the insurance industry (including pension insurance) and is not adapted to assess the level of risk.

The article presents the key positions of the author’s theory of actuarial calculations, which offers a generalized approach to solving actuarial problems in various types of economic activities using a variety of information about the risk. The basic idea of the theory is that any result of actuarial calculations can be expressed in terms of quantiles of the future net loss associated with the realization of risk.

The estimation of each quantile can be considered as a special case of evaluation of unobserved economic values, such as cost, projected profit, and so forth. The problem of estimating these values lies with the multivariance of the original data and methods, as a result of which different specialists often receive significantly divergent estimates.

For this, the author proposed to use the methodology of evaluation, which consists in obtaining the median of all single estimates that can be obtained from representative samples of possible scenarios, evaluation models and values of the original data. This methodology can be used to estimate the quantiles of the future loss, and the complexity of the original data involves the use of numerical methods, in particular, the Monte Carlo method.

The authors tested research tools on the example of solving the problem of quantitative characteristic of credit risk. They also constructed and estimated the mathematical and statistical model of loss from the default of the borrower, and proved the possibility of sufficient repeatability and reproducibility of results. The data of state statistics, financial statements of credit institutions, model estimates served as initial data.

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