On Premium Estimation Using the C&RT/Poisson Model and Its Extensions

Abstract

Premium estimation is a key concept in insurance mathematics. Estimation of the mean andvariance of a total claim amount of a portfolio can be considered as necessary prerequisites for this. Inturn, dividing the portfolio into homogeneous subportfolios can be considered as a rst step towards ndingthose estimates. We consider the problem of estimating the claim intensity and propose a regressiontrees based approach for clustering the portfolio into homogeneous subportfolios in a situation where thedurations of the policies dier and overdispersion is present. Several other generalizations are discussed.A case study involving Estonian casco insurance is included.