EXTENSION OF THE CLASSIC RISK MODEL BY A HAWKES PROCESS AND A PHASE-TYPE DISTRIBUTION

This article is an extension of the classic risk model by using the Hawkes process for modeling the claims counting process. In this model, we consider that the amount of claims is independent and identically distributed according to a standard phase law. We establish integro-differential equations, Laplace transforms of the function updated Gerber-Shiu penalty and probability of ruin. Closed and complex formulas of the Gerber-Shiu function and the probability of ruin are subsequently exhibited.