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On the probability of reaching a barrier in an Erlang(2) risk process. (English) Zbl 1274.91246

Summary: 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, \(\chi(u,b)\). Our main contribution is the generalization obtained in the computation of \(\chi(u,b)\) for the case of interoccurrence time between claims distributed as \(\text{Erlang}(2,\beta)\) and the individual claim amount as \(\text{Erlang}(n,\gamma)\).

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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