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Poisson-Gamma mixture processes and applications to premium calculation. (English) Zbl 07571105

Summary: 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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
37C75 Stability theory for smooth dynamical systems

Software:

Python; CreditRisk+
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Full Text: DOI

References:

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