Research On Rate Making When Claim Number And Claim Amount Are Related

The traditional model is based on the assumption that the number of claims and the amount of claims are independent.In practice,claim number and claim size are often dependent.So in this paper we consider rate making when claim number and claim amount are related.Actually,in a given time period,the claim sizes of a policy holder are not independent,so when we study the dependence between claims number and claims size,we fit generalized linear model to the number of claims,but employ generalized linear mixed model to fit the claim amount.The correlation between the number of claims and the claim amount is clearly expressed in the generalized linear mixed model so that the method of determining the rate is more in line with the actual situation.We adopt the maximum likelihood estimation method based on EM to estimate the parameters of generalized linear mixed model and generalized linear model.Specifically,we construct a Markov Chain whose invariant distribution is the conditional distribution of the random effect by MH algorithm,and approximate the expectation in the EM algorithm by Monte Carlo approximation.In order to eliminate the randomness of parameters,we estimate the parameters using 100 data sets.In order to highlight the relationship between claim size and the claim number,we have compared the results with the model assuming claim number and claim size are independent.When these two variables are negative associated,the net premium is lower than the net premium calculated under the independence condition.When these two variables have the positive correlation,the net premium would be higher than net premium under the condition of independence.Therefore,it is important to consider the correlation between the number of claims and the amount of claim in the rate pricing.