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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
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/4141346
Page Count: 12
You can always find the topics here!Topics: Poisson process, Financial risk, Brownian motion, Mathematics, Net profits, Random variables, Laplace transformation, Insurance
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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.
Journal of Applied Probability © 2004 Applied Probability Trust