A perturbed risk model with constant interest and periodic barrier dividend strategy

Abstract

This paper studies the discounted Gerber-Shiu type function for a perturbed actuarial risk model with interest and periodic dividend strategy. Under the assumption of exponentially distributed inter-observation times, some integro-differential equations of the discounted Gerber-Shiu type function at ruin are presented. For exponential claim amounts, explicit expressions satisfied by the Laplace transforms of ruin time are provided and some numerical examples are investigated to demonstrate our results.

Keywords:

• Gerber-Shiu function
• Interest rate
• Laplace transform of ruin time
• Perturbed compound Poisson risk model
• Periodic dividend strategy

Acknowledgments

The authors wish to express their sincere appreciation to the support of the National Natural Science Foundation of China (11761014), The Guangxi Natural Science foundation (2016GXNSFBA380035, 2017GXNSFAA198243, 2018GXNSFAA281016), Open Foundation for Key Laboratories of Mathematics and Statistical Models in Universities of Guangxi (2017GXKLMS002) and the Youth Science Foundation of Guangxi Normal University (17A4).