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Document Details :
Title: Ruin Probabilities for Two Classes of Risk Processes
Author(s): LI, S. , GARRIDO, J.
Journal: ASTIN Bulletin
Volume: 35 Issue: 1 Date: May 2005
We consider a risk model with two independent classes of insurace risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes with generalized Erlang claim inter-arrival times. The Laplace transform of the non-ruin probability is derived from a system of integro-differential equations. Explicit results can be obtained when the initial reserve is zero and the claim sseverity distributions of both classes belong to the Kn family of distributions. A relation between the ruin probability and the distribution of the supremum before ruin is identified. Finally, the Laplace transform of the non-ruin probability of a perturbed Sparre Andersen risk model with generalized Erlang claim inter-arrival times is derived when the compound Poisson process converges weakly to a Wiener process.