Collective risk model: Poisson–Lindley and exponential distributions for Bayes premium and operational risk

Abstract

In this paper the collective risk model with Poisson–Lindley and exponential distributions as the primary and secondary distributions, respectively, is developed in a detailed way. It is applied to determine the Bayes premium used in actuarial science and also to compute the regulatory capital in the analysis of operational risk. The results are illustrated with numerous examples and compared with other approaches proposed in the literature for these questions, with considerable differences being observed.

Keywords:

• Bayes premium
• collective risk model
• operational risk
• Poisson–Lindley distribution

AMS Subject Classification :

• 62C10
• 62P05

Acknowledgements

AHB is funded by Ministerio de Educación y Ciencia (projects SEJ2006-12685 and ECO2009-14152). EGD is funded by Ministerio de Educación y Ciencia, Spain, under project SEJ2006-12685. The authors thank an editor and a reviewer for their valuable comments which have helped in improving the paper.