Uniform asymptotics for a risk model with constant force of interest and a random number of delayed claims

Abstract

Consider an insurance risk model with constant force of interest under the assumption that an immediate claim is accompanied by a random number of delayed claims. In the presence of heavy tails on claim distributions and dependence structures among modelling components, we study the uniform asymptotics for an insurer's ruin-related quantities, where the uniformity holds for all time horizons varying in a relevant interval.

Keywords:

• Uniform asymptotics
• ruin probability
• delayed claims
• dependence structures

Mathematics Subject Classifications (2020)::

• 62E20
• 62P05
• 91B05

Acknowledgments

The authors would like to thank the editors and the anonymous referees for their efforts on the early version of this paper.

Disclosure statement

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

Additional information

Funding

The research was partly supported by the National Natural Science Foundation of China (No. 12371471), the Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 20YJCZH034), the Natural Science Foundation of the Jiangsu Higher Education Institutions (No. 22KJA110001), the Open Project of Jiangsu Key Laboratory of Financial Engineering (No. NSK2021-05), and the Qing-Lan Project of Jiangsu Province.