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December 2012 Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments
Xuemiao Hao, Qihe Tang
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J. Appl. Probab. 49(4): 939-953 (December 2012). DOI: 10.1239/jap/1354716649

Abstract

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y0=x > 0, evolves according to dYt= Yt- dRt -dPt for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x→∞, which confirms Paulsen's conjecture.

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Xuemiao Hao. Qihe Tang. "Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments." J. Appl. Probab. 49 (4) 939 - 953, December 2012. https://doi.org/10.1239/jap/1354716649

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1255.91180
MathSciNet: MR3058980
Digital Object Identifier: 10.1239/jap/1354716649

Subjects:
Primary: 91B30
Secondary: 60G51, 91B28

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 4 • December 2012
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