Bayesian Estimation of Event Probability in Accident Insurance

Knowledge of the probability of an insured event is the basis for the valuation of the products in life and non-life insurance companies. For estimation of event probability in insurance practice the most often use the historical data from a large portfolio of insurance policies. The classical approach to point estimation of the event probability is by proportion of occurrence of the event in large portfolio of policies. The objective of this paper is to present Bayesian estimation of selected binomial proportions in accident insurance. The classical approach to point estimation treats parameters as something fixed but unknown. The essential difference in the Bayesian approach to inference is that parameters are treated as random variables and therefore they have probability distributions. In Bayesian approach to estimation we should always start with a priori distribution for unknown parameter, precise or vague according to the information available. In this paper we have derived an algorithm for such a priori estimation of the binomial probability, which allows Bayesian estimates with less square error compared with classical estimates. In article the suggested algorithm has been applied on the data submitted by the Decree No. 20/2008 to the National Bank of Slovakia from insurance companies giving exposure to the accident risk.