Dubinina S. Bayesian methods of simulating actuarial processes and risk estimation of insurance company

The research is directed towards forecasting of insurance payments in respective cases and estimation of operational risk for insurance companies. The necessary mathematical models were developed in the form of generalized linear models (GLM) and Bayesian networks what is a new scientific element of the research. An adaptation procedure based on extreme value theory was proposed for processing degenerated statistical samples for constructing GLM. New generalized linear models were constructed for the selected actuarial processes that provide for a possibility of estimating high quality short term forecasts regarding insurance payments. It was established that the best model was the one with gamma distribution and logarithmic link function. To get the possibility for probabilistic estimation of operational risks the model in the form of Bayesian network was developed using a set of selected variables. The complex model developed provides a possibility for timely prevention of insurance company bankruptcy and perform an analysis for necessary volume of insurance payments according to the specific insurance policies. All computational experiments were performed with the decision support system designed and implemented by the author. The system constitutes a handy data analysis instrument for insurance company managers and can be easily extended with new functions.