On the probability of reaching a barrier in an Erlang(2) risk process

In this paper the process of aggregated claims in a non-life insurance portfolio as defined in the classical model of risk theory is modified. The Compound Poisson process is replaced with a more general renewal risk process with interoccurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ (u, b). Our main contribution is the generalization obtained in the computation of χ (u, b) for the case of interoccurrence time between claims distributed as Erlang(2, β) and the individual claim amount as Erlang (n, γ).