Bonus--malus systems with different claim types and varying deductibles

TL;DR

This paper introduces and analyzes bonus-malus insurance systems with multiple claim types and variable deductibles, exploring their properties, restrictions, and specific cases with numerical examples.

Contribution

It proposes new bonus-malus systems with claim-type differentiation and varying deductibles, and studies their fundamental properties and implementation restrictions.

Findings

Varying deductibles can be integrated into bonus-malus systems under specific conditions.

Restrictions on deductible variation depend on claim types and policyholder levels.

Numerical examples illustrate the application and effects of the proposed systems.

Abstract

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported claims. We introduce such bonus-malus systems and study their basic properties. In particular, we investigate when it is possible to introduce varying deductibles, what restrictions we have and how we can do this. Moreover, we deal with the special case where varying deductibles are applied to the claims reported by policyholders occupying the highest level in the bonus-malus scale and consider two allocation principles for the deductibles. Finally, numerical illustrations are presented.