Risk models with premiums adjusted to claims number



Li, Bo, Ni, Weihong and Constantinescu, Corina ORCID: 0000-0002-5219-3022
(2015) Risk models with premiums adjusted to claims number. Insurance: Mathematics and Economics, 65 (C). pp. 94-102.

[img] Text
Latent Risks in Mixed Compound Poisson Ruin Models.pdf - Submitted version

Download (330kB)

Abstract

Classical compound Poisson risk models consider the premium rate to be constant. By adjusting the premium rate to the claims history, one can emulate a Bonus–Malus system within the ruin theory context. One way to implement such adjustment is by considering the Poisson parameter to be a continuous random variable and use credibility theory arguments to adjust the premium rate a posteriori. Depending on the defectiveness of this random variable, respectively referred to as ‘unforeseeable’ (defective) versus ‘historical’ (non-defective) risks, one obtains different relations between the ruin probability with constant versus adjusted premium rate. A combination of these two kinds of risks also leads to a relation between the two ruin probabilities, when the a posteriori estimator of the number of claims is carefully chosen. Examples for specific claim sizes are presented throughout the paper.

Item Type: Article
Additional Information: ## TULIP Type: Articles/Papers (Journal) ##
Uncontrolled Keywords: ruin probability, Mixed Poisson process, Bonus-Malus, Bayesian estimation, Lukacs' theorem
Depositing User: Symplectic Admin
Date Deposited: 07 Dec 2018 14:28
Last Modified: 19 Jan 2023 01:09
DOI: 10.1016/j.insmatheco.2015.09.001
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3029709