The Annals of Applied Probability

Ruin probabilities and decompositions for general perturbed risk processes

Miljenko Huzak, Mihael Perman, Hrvoje Šikić, and Zoran Vondraček

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We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, with the perturbation being a spectrally negative Lévy process with zero expectation. We derive a Pollaczek–Hinchin type formula for the survival probability of that risk process, and give an interpretation of the formula based on the decomposition of the dual risk process at modified ladder epochs.

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Ann. Appl. Probab., Volume 14, Number 3 (2004), 1378-1397.

First available in Project Euclid: 13 July 2004

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G51: Processes with independent increments; Lévy processes 60J75: Jump processes 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 91B30: Risk theory, insurance

Risk theory ruin probability Pollaczek–Hinchin formula subordinator spectrally negative Lévy process


Huzak, Miljenko; Perman, Mihael; Šikić, Hrvoje; Vondraček, Zoran. Ruin probabilities and decompositions for general perturbed risk processes. Ann. Appl. Probab. 14 (2004), no. 3, 1378--1397. doi:10.1214/105051604000000332.

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