The Polya–Aeppli process and ruin problems

The Polya–Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Polya–Aeppli process. It is called a Polya–Aeppli risk model. The problem of finding the ruin probability and the Cramer–Lundberg approximation is studied. The Cramer condition and the Lundburg exponent are defined. Finally, the comparison between the Polya–Aeppli risk model and the corresponding classical risk model is given.