# On monotone likelihood ratio of stationary probabilities in bonus-malus systems

On monotone likelihood ratio of stationary probabilities in bonus-malus systems AbstractBonus-malus system is an often used risk management tool in the insurance industry, and it is usually modeled with Markov chains. Under mild conditions it can be stated that the bonus-malus system converges to a unique stationary distribution in the long run. The maximum likelihood ratio property is a well-known statistical concept and we define it for the stationary distribution of a bonus-malus system. For two special cases we could justify it algebraically. For other cases we describe a numerical method with which we can test this property in any case. With the help of the described method, we checked this property for cases that appear in actuarial practice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure Mathematics and Applications de Gruyter

# On monotone likelihood ratio of stationary probabilities in bonus-malus systems

, Volume 30 (3): 11 – Oct 1, 2022
11 pages

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Publisher
de Gruyter
Copyright
© 2022 Kolos Csaba Ágoston et al., published by Sciendo
eISSN
1788-800X
DOI
10.2478/puma-2022-0023
Publisher site
See Article on Publisher Site

### Abstract

AbstractBonus-malus system is an often used risk management tool in the insurance industry, and it is usually modeled with Markov chains. Under mild conditions it can be stated that the bonus-malus system converges to a unique stationary distribution in the long run. The maximum likelihood ratio property is a well-known statistical concept and we define it for the stationary distribution of a bonus-malus system. For two special cases we could justify it algebraically. For other cases we describe a numerical method with which we can test this property in any case. With the help of the described method, we checked this property for cases that appear in actuarial practice.

### Journal

Pure Mathematics and Applicationsde Gruyter

Published: Oct 1, 2022

Keywords: Bonus-malus system; mixed integer programming; 60J22

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