Uniform asymptotics for discounted aggregate claims in dependent multi-risk model

ABSTRACT

In this paper, we consider a nonstandard renewal multi-risk model where a company has n types of independent insurance contracts and each contract has some dependent claims and stochastic return. The price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to the class of $\mathcal{C}$, we can get some asymptotic formulae for the tail probability of n types contracts’ discounted aggregate claims and ruin probabilities, holding uniformly for some finite horizons.

KEYWORDS:

• Consistently varying tail
• Dependence
• Discounted aggregate claims
• Lévy process
• Multi-risk model
• Uniformity.

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B30
• 60G51
• 60K05

Acknowledgments

The research of the first author is supported by the National Natural Science Foundation of China (Grant Nos. 11571058). The second author is supported by the National Natural Science Foundation of China (Grant Nos. 11371077).

Additional information

Funding

National Natural Science Foundation of China(10.13039/501100001809, 11371077, 11571058)