Asymptotics for sum-ruin probabilities of a bidimensional risk model with heavy-tailed claims and stochastic returns

Abstract

This paper considers a bidimensional risk model with geometric Lévy price processes and dependent heavy-tailed claims, where the two claim-number processes generated by the two different lines of business are almost arbitrarily dependent. When the distributions of the claims are subexponential with a positive lower Matuszewska index, an asymptotic formula for the finite-time sum-ruin probability is derived, which has a more transparent form when the distributions of the claims are regularly-varying-tailed and the two claim-number processes are homogeneous Poisson processes. Some simulation studies are conducted to verify the accuracy and sensitivity of the asymptotic result by employing the crude Monte Carlo method.

Keywords:

• Bidimensional risk model
• finite-time sum-ruin probability
• dependent heavy-tailed claim
• geometric Lévy price process
• Crude Monte Carlo method

Mathematics Subject Classification (2020):

• Primary 62P05
• Secondary 62E10

Acknowledgments

The authors wish to thank the editor and the referees for their careful reading and exceedingly valuable comments on an earlier version of this paper, which have helped us significantly improve the quality of the manuscript.

Availability of data and materials

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper was supported by National Natural Science Foundation of China (No. 11401415).