Risk models with premiums adjusted to claims number

Bo Li, Weihong Ni and Corina Constantinescu

Insurance: Mathematics and Economics, 2015, vol. 65, issue C, 94-102

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.

Keywords: Ruin probability; Mixed Poisson process; Bonus–Malus; Bayesian estimation; Lukacs’ theorem (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:65:y:2015:i:c:p:94-102

DOI: 10.1016/j.insmatheco.2015.09.001

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