Poisson-Gamma mixture processes and applications to premium calculation

Shujin Wu

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 17, 5913-5936

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.

Date: 2022
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DOI: 10.1080/03610926.2020.1850791

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