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.
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 |