Uncertainty analysis and risk modeling in insurance

Abstract

There are various definitions of risks, depending on the used approach, context and the given aspect. It is considered by some authors that risk and uncertainty are two completely independent concepts, while others see these terms as highly interdependent. The notion of uncertainty implies that there is a possible spectrum of events that can happen in the future, however without indications that they will really happen or have a relative effect. On the other hand, the term risk implies the possibility to list events that may occur in the future, and that the likelihood of realization can be determined for the each one of them. The uncertainty is also described as the absence of information in a decision-making process and implies the assessment of a particular situation, alternative solutions, possible results and consequences, etc. In extreme situations, uncertainty can be characterized as the lack of information or knowledge about a particular problem or in the decision-making process. Risk assessment is a complex task that requires a great deal of responsibility, so the actuary needs to be familiar with the application of the statistical theory of credibility and its basic methods. In this study basic credibility procedures, with appropriate calculations, are presented. Actuarial science requires a combination of academic rigor and business practice. Actuaries rarely use the theory of credibility in a purely statistical way. The subset of the observed population has characteristics that are not completely determined, so the actuarial assessment is necessary in order to determine the possible purpose of these characteristics. In most cases, the effects of population characteristics are known to some extent, but there is insufficient data to eliminate the need for a particular estimation in the selection of probability distribution and parameters. Numerous examples from practice indicate that there is often uncertainty about input data necessary for making certain decisions. Decisions are often made on the basis of experience, intuition, subjective assessment of parameters that they appear in these situations. Fuzzy mathematical modeling is used in situations of uncertainty, uncertainty, and subjective evaluation.