Ruin probabilities for competing claim processes

Abstract

Let C 1 , C 2 ,…, 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.