Some Bayesian Premiums Obtained by Using the Common Effect in Claim Dependence Model

Tippatai Pongsart, Kiat Sangaroon, Pairote Sattayatham

Abstract

In risk theory, insurance premiums are calculated from a model using claim data which can be constructed in two dimensions with one dimension representing time and the other representing distinct insured individuals. Several models found in the literature allow for independent assumptions across different risks for the sake of convenience and mathematical tractability. However, these assumptions may be violated in some practical situations. In this paper, modeling claim dependence is built under the common effect. According to the model, we express the expected claims given the history of all observable claims (Bayesian premiums) in explicit form with lognormal claim amounts distribution.