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. ISSN 0167-6687, 1873-5959

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:	01 Mar 2026 00:44
DOI:	10.1016/j.insmatheco.2015.09.001
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029709
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