Sequential Monte Carlo samplers to fit and compare insurance loss models

Abstract

Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the ‘body’ and the other for the ‘tail’ of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset.

Keywords:

• Composite model
• Bayesian statistics
• sequential Monte Carlo sampler

MSC 2010:

• 60G55
• 60G40
• 12E10

Acknowledgments

The author thanks the associate editor and the two anonymous reviewers for their insightful comments which greatly improved the manuscript. The author's work is conducted within the Research Chair DIALog under the aegis of the Risk Foundation, an initiative by CNP Assurances.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 https://pypi.org/project/bayes-splicing/

2 scipy.integrate method from the scipy python library https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html

3 tea package documentation

Additional information

Funding

This work was supported by the CNP Assurance  through a "Chaire de recherche" named DIALOG, https://chaire-dialog.fr/.