Asymptotics for the random time ruin probability with non stationary arrivals and Brownian perturbation

Abstract

In this paper, we consider a risk model with heavy-tailed claims and Brownian perturbation. Assuming that the distribution function of claim-size is subexponential, and the arrival process of claims is a non stationary process satisfying the principle of large deviation, the asymptotic formula for the ruin probability of this risk model at random time is obtained.

Keywords:

• Brownian perturbation
• Cox process
• Hawkes process
• non stationary arrival process
• ruin probability
• subexponential class

AMS MATHEMATICS SUBJECT CLASSIFICATION:

• 62P05

Acknowledgments

The authors are very grateful to reviewers for their thorough reading of the paper and constructive suggestions, by which both the statements and the proofs of Lemma 3.3 and Theorem 2.1 have been significantly improved.

Additional information

Funding

Project supported by the National Social Science Foundation of China (No. 20BTJ050).