Asymptotics for ruin probabilities of a dependent delayed-claim risk model with general investment returns and diffusion

Abstract

In this paper, we study a delayed-claim insurance risk model perturbed by diffusion with general investment returns, in which each main claim may induce a delayed claim. Assume that the main claim sizes follow a one-sided linear process with independent and identically distributed step sizes. Furthermore, we assume that the step sizes and the inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a bivariate Sarmanov distribution, and so do the delayed claim sizes and corresponding delayed times. In the presence of heavy tails, asymptotic upper and lower bounds for ruin probabilities are obtained. Finally, in order to verify the accuracy of our results, we conduct numerical simulations by Crude Monte Carlo (CMC) method.

Keywords:

• One-sided linear process
• dependence structure
• delayed claim
• ruin probability

Mathematics Subject Classifications:

• 62P05
• 62E20

Acknowledgements

The authors are most grateful to the reviewers and the editors for their valuable comments on an earlier version of this paper.

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [No. 71871046], the National Natural Science Foundation of China [No. 72033002], the Science and Technology Plan Key Research and Development Project of Sichuan Province [No. 2023YFSY0007], the Science and Technology Plan Key Research and Development Project of Sichuan Province [No. 2023YFG0114], and the Key Research and Development Supported Project of Chengdu [No. 2021YF0800019GX].