Abstract: Premium pricing refers to the process by which an actuary determines a reasonable premium based on the distribution characteristics of the risk. In order to improve the competitiveness of insurance companies, the premiums must be scientific and reasonable and matches the policy risks. However, due to the complexity of risk factors, structural changes in policy risk often lead to changes in premiums, and the detection of premiums is one of the important issues for insurance companies. In this paper, the change point detection model of the exponential premium principle is established. Based on the statistical inference methods in change point theory, the statistic of detecting the change point of the risk premium is proposed, and the estimation of the change point position of the premium is given. Furthermore, the large sample properties and the convergence speed of the estimator are proved. Finally, the numerical simulation method is used to verify the convergence of the statistics, and the accuracy difference of the premium change detection caused by different positions is compared. The method presented in this paper can provide reference value and basis for the insurance company's premium pricing and change detection.

Key words: exponential premium principle, risk premium, change point, hypothesis test, consistency