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Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Xuemiao Hao  and
Qihe Tang
Xuemiao Hao*
Affiliation:
University of Manitoba
Qihe Tang*
Affiliation:
University of Iowa
*
∗ Postal address: Asper School of Business, University of Manitoba, 181 Freedman Crescent, Winnipeg, Manitoba R3T 5V4, Canada. Email address: xuemiao.hao@ad.umanitoba.ca
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: qihe-tang@uiowa.edu
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Abstract

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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.

Keywords

(extended) regular variationfinite-time and infinite-time ruin probabilitiesLévy processstochastic difference equationtail probability

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 939 - 953
Copyright
© Applied Probability Trust 

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