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Ruin probabilities for competing claim processes. (English) Zbl 1065.60100

Summary: Let \(C_1,C_2,\dots, C_m\) be independent subordinators with finite expectations and denote their sum by \(C\). Consider the classical risk process \(X(t)= x+ ct- C(t)\). The ruin probability is given by the well-known Pollaczek-Khinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators \(C_i\). Formulae for the probability that ruin is caused by \(C_i\) are derived. These formulae can be extended to perturbed risk processes of the type \(X(t)= x+ ct- C(t)+ Z(t)\), where \(Z\) is a Lévy process with mean 0 and no positive jumps.

MSC:

60J25 Continuous-time Markov processes on general state spaces
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References:

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