Asymptotic ruin probabilities for a two-dimensional risk model with dependent claims and stochastic return

Abstract

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions.

KEYWORDS:

• Asymptotic independence
• Lévy process
• regular variation
• ruin probability
• stochastic return

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62P05
• Secondary 62E10
• 91B30

Acknowledgments

The author is very grateful to the anonymous reviewers for their thorough reading of the paper and constructive suggestions.

Disclosure statement

The author declared that he has no conflict of interest.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Numbers: 11871289, 11931018 and 11911530091).