The Claim Number Process as a Markov Process

The characterizations of the Poisson process given in the previous chapter show that the Poisson process is a very particular claim number process. In practical situations, however, the increments of the claim number process may fail to be independent or fail to be stationary or fail to be Poisson distributed, and in each of these cases the Poisson process is not appropriate as a model. The failure of the Poisson process raises the need of studying larger classes of claim number processes.