Poisson-Gamma mixture processes and applications to premium calculation

Abstract

In the paper, Poisson-Gamma mixture process is first brought forward, which is dynamically expanded from the well-known Poisson-Gamma mixture model. Some properties on Poisson-Gamma mixture process are presented, including the distribution of increment, Markov property, infinitesimal generator, joint density function of jump/waiting times, and the limit distribution of compound Poisson-Gamma mixture process, etc., which provide a thorough grounding in application of Poisson-Gamma mixture process. At last, some premium calculation principles are presented to show the application of Poisson-Gamma mixture process, which include expected value premium, stop-loss premium, mean-variance premium, and exponential premium.

Keywords:

• Mixture model
• Poisson process
• Gamma process
• premium calculation

2000 MR Subject Classification:

• 60H10
• 37C75

Acknowledgements

The author would like to thank the anonymous referees for their careful review, comments, and feedback on the manuscript.

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China (No.11471120) and the Science and Technology Commission of Shanghai Municipality (Grant No. 19JC1420100).