Abstract
In this paper we introduce a mixed Polya-Aeppli process with shifted gamma mixing distribution and call it an Inated-parameter Delaporte process (I-Delaporte). We derive the pro bability mass function, recursion formulas and some basic properties. Then we de ne the process as a pure birth process and derive differential equations for the probabilities. As application, we consider a risk model in which the claim counting process is the de ned I-Delaporte process. For the defined risk model we derive the joint distribution of the time to ruin and the de cit at ruin as well as the ruin probability. We discuss in detail the particular case of exponentially distributed claims.
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