Some Aspects of Cumulative Risk

The classical treatment of stochastic models in non-life insurance is to first derive the well-known Poisson distribution by considering the question of how many claims take place during a definite period. In deriving this distribution the following three assumptions are made: ( I) The population studied is homogeneous. (II) The occurrence of a claim is a rare event, viz. in an infinitesimal time interval It, t + At], the probability of more than one occurrence must be of the order of magnitude (variable). (III) The occurrence of any later claim is not influenced by previous ones (no contagion).