A NUMERICAL ALGORITHM FOR FINDING THE RUIN PROBABILITY IN THE CRAMÉR-LUNDBERG MODEL
Urgency of the research. Recently, there has been a rapid increase in interest in computer techniques of forecasting in the insurance business. Such forecasting can be used, in particular, to determine the pricing policy of insurance companies. Target setting. Currently, there arises the need to develop simple and precise numerical algorithms for estimating the probability of ruin, which can be effectively implemented by computer software. Actual scientific researches and issues analysis. At the moment, an extensive toolkit of numerical methods for evaluating various characteristics of insurance risk processes (ruin probabilities in the finite and infinite time horizons, expectation and variance of the time of ruin, etc.) has been accumulated. Uninvestigated parts of general matters defining. Existing techniques are either too complicated to implement, or demonstrate an insufficient accuracy of estimation. The research objective. The development of a numerical algorithm which refines the classical de Vylder approximation for estimating the ruin probability on the infinite time horizon in the Cramér-Lundberg insurance risk model, as well as the study of the accuracy of this algorithm based on Beekman's formula. The statement of basic materials. In the article, we develop a new method for approximate determination of the probability of degeneration of the Cramér-Lundberg insurance risk process on the infinite time horizon. This method refines the approximation proposed by F. de Vylder, by replacing the reference exponential distribution of insurance payments by a mixture of two exponential ones. Computer simulation shows a much higher accuracy of the proposed algorithm compared with the de Vylder’s approach. Conclusions. The proposed algorithm allows to estimate the ruin probability of an insurance company in the CramérLundberg model. The method is based on replacing the insurance risk process with another risk process, for which insurance payments are distributed according to the law, which is a mixture of two exponential distributions. The advantages of the developed method include its much higher accuracy in comparison with the de Vylder approximation. The features of the method are the higher complexity of implementation due to the need for an approximate solution of a system of nonlinear equations, and also that this system has suitable solutions not for any distribution of insurance payments.