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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 13 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1089736289

Digital Object Identifier
doi:10.1214/105051604000000332

Mathematical Reviews number (MathSciNet)
MR2071427

Zentralblatt MATH identifier
1061.60075

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1089736289


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