Asymptotic behavior for sum ruin probability of a generalized bidimensional risk model with heavy-tailed claims

Abstract

This paper considers a generalized bidimensional continuous-time risk model with subexponential claims, constant force of interest and Brownian perturbations, where the claim sizes from each line of business are dependent according to some dependence structure and the two components of each claim-inter-arrival-time vector are arbitrarily dependent. Some asymptotic presentations are shown for the finite-time sum ruin probability defined as the probability that the sum of two surplus processes generated by two lines of business goes below zero over a time horizon $[0,t].$ Particularly, the claim-number processes from different lines of business can be arbitrarily dependent when the claim sizes are long-tailed and dominatedly-varying-tailed.

Keywords:

• Bidimensional risk model
• heavy-tailed claim
• sum ruin probability
• arbitrarily dependent

Acknowledgements

The authors would like to express their great gratitude to the referees for their constructive and insightful suggestions which help to improve the presentation of this paper greatly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

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