Large deviations for the stochastic present value of aggregate claims in the nonstandard compound renewal risk model with widely upper Orthant dependent claims

Abstract

Recently, Jiang et al. (Statist. Probab. Lett. 101, 83–91) obtained the asymptotic formulas for the large deviations for the stochastic present value of aggregate claims in the renewal risk model with Pareto-type claims and stochastic return on investments, where the price process of the investment portfolio is described as a geometric Lévy process. In the paper, we extend the above results to a nonstandard compound renewal risk model with widely upper orthant dependent and dominatedly-varying-tailed claims.

Keywords:

• Asymptotics
• Large deviation
• Compound renewal model
• Widely upper orthant dependence
• Dominated variation

MATHEMATICS SUBJECT CLASSIFICATIONS 2010:

• 60F10
• 62P05
• 91B30

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments on the early version of this paper.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China (NOs. 11501295 and 11871289), the Postdoctoral Science Foundation of China (NO. 2015M580415), the Natural Science Foundation of Jiangsu Province of China (NO. BK20151459), the Social Science Foundation of Jiangsu Province of China (NO. 16GLC006), the Postdoctoral Science Foundation of Jiangsu Province of China (NO. 1501004B) and the Qing-Lan Project of Jiangsu Province.