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Ruin Probabilities for Competing Claim Processes

Miljenko Huzak, Mihael Perman, Hrvoje Šikić and Zoran Vondraček
Journal of Applied Probability
Vol. 41, No. 3 (Sep., 2004), pp. 679-690
Stable URL: http://www.jstor.org/stable/4141346
Page Count: 12
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Ruin Probabilities for Competing Claim Processes
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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 Ci. Formulae for the probability that ruin is caused by Ci 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.

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