<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Bonus-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.</p>
</abstract>

Bonus-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.

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

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On monotone likelihood ratio of stationary probabilities in bonus-malus systems"}

Bonus-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...

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

Published Online: Nov 07, 2022

Page range: 43 - 53

Received: Nov 04, 2021

DOI: https://doi.org/10.2478/puma-2022-0023

Keywords
Bonus-malus system, mixed integer programming

© 2022 Kolos Csaba Ágoston et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Nov 07, 2022

Page range: 43 - 53

Received: Nov 04, 2021

DOI: https://doi.org/10.2478/puma-2022-0023

KeywordsBonus-malus system, mixed integer programming

© 2022 Kolos Csaba Ágoston et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Bonus-malus system, mixed integer programming