Claramunt, M. Mercè; Mármol, M. Teresa; Lacayo, Ramon On the probability of reaching a barrier in an Erlang(2) risk process. (English) Zbl 1274.91246 SORT 29, No. 2, 235-248 (2005). 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 \(\text{Erlang}(n,\gamma)\). Cited in 1 Document MSC: 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:risk theory; Erlang distribution; upper barrier; ordinary differential equation; boundary conditions PDFBibTeX XMLCite \textit{M. M. Claramunt} et al., SORT 29, No. 2, 235--248 (2005; Zbl 1274.91246) Full Text: EuDML Link