Asymptotics for ruin probabilities in a bidimensional discrete-time risk model with dependent and consistently varying tailed net losses

Abstract

Consider an insurer who operates two lines of businesses and hence receives two types of insurance net losses. In the bidimensional discrete-time risk model with a constant interest rate, the net loss vectors from the two business lines form a sequence of independent and identically distributed real-valued random vectors. We propose a bidimensional extended regularly varying structure in terms of survival copulas to model the dependence between the two components of each net loss vector, which includes not only asymptotic independence but also asymptotic dependence. Under the framework of consistent variation, we obtain several (uniformly) asymptotic formulas for various ruin probabilities. In particular, the investigation of random-time ruin probabilities unifies and extends the results on both finite-time and infinite-time ruin probabilities. Some numerical studies are also performed to check the accuracy of our obtained asymptotic results.

Keywords:

• Asymptotics
• bidimensional discrete-time risk model
• ruin probability
• bidimensional extended regularly varying dependence
• consistent variation

Mathematics Subject Classifications:

• 62P05
• 62E20
• 91B05

Acknowledgements

The authors would like to thank the anonymous referees and the associate editor for their suggestive comments and very careful reading of the paper.

Disclosure statement

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

Availability of data and materials

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

Additional information

Funding

Yang Yang acknowledges the financial support by the National Social Science Fund of China (No. 22BTJ060), the Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 20YJA910006), Natural Science Foundation of Jiangsu Province of China (No. BK20201396), and Natural Science Foundation of the Jiangsu Higher Education Institutions (No. 23KJA110002). Qi Su acknowledges the financial support by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX22_2208).