Journal of Applied Probability
- J. Appl. Probab.
- Volume 49, Number 4 (2012), 939-953.
Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments
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.
J. Appl. Probab., Volume 49, Number 4 (2012), 939-953.
First available in Project Euclid: 5 December 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 91B30: Risk theory, insurance
Secondary: 60G51: Processes with independent increments; Lévy processes 91B28
Hao, Xuemiao; Tang, Qihe. Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments. J. Appl. Probab. 49 (2012), no. 4, 939--953. doi:10.1239/jap/1354716649. https://projecteuclid.org/euclid.jap/1354716649