The infinite-time ruin probability for a bidimensional renewal risk model with constant force of interest and dependent claims

ABSTRACT

This article studies a continuous-time bidimensional risk model, in which an insurer simultaneously confronts two kinds of claim sharing a common renewal claim-number process. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution with extended regularly varying margins, we derive an explicit asymptotic formula for the corresponding infinite-time ruin probability.

KEYWORDS:

• Asymptotics
• Bidimensional renewal risk model
• Frlie–Gumbel–Morgenstern distribution
• Ruin probability
• Extended regular variation

MATHEMATICS SUBJECT CLASSIFICATION::

• Primary 62P05
• Secondary 62E10
• 91B30

Acknowledgments

The author is very grateful to an anonymous reviewer for his/her very thorough reading of the article and valuable suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11371020) and the project RARE–318984 (an FP7 Marie Curie IRSES Fellowship).