Abstract
This paper sets out to accomplish the following:
i. Based on set assumptions, we vectorially define the number of policyholders per merit class by year of enrollment and number of years elapsed. Thus calculating the distribution of class sizes for a year in which the system has reached a steady state.
ii. We calculate the class-size distribution for each risk level by introducing multiple risk levels for policyholders.
iii. We calculate insurance premiums based on a bonus-malus system and a flat-rate system, taking into consideration the premium increase/reduction rate for each class. In this way, we ascertain the characteristics of the bonus-malus system.
iv. We calculate the loss ratio for each merit class based on the distribution of policyholders at each risk level in each merit class.
We arrived at the following conclusions: i. Compared to a flat-rate system, a bonus-malus system is better able to reflect risk levels in insurance premiums.
ii. When rate classes are subdivided, the premium differential attributable to rate class between policyholders at the same risk level is less pronounced under a bonus-malus system than under a flat-rate system. But even bonus-malus systems cannot fully absorb all differences in policyholder risk levels.
iii. Based on this paper’s assumptions, we determined the relationship between premium increase/reduction rates and loss ratios for each merit class.
KEYWORDS: Bonus-malus system; rate class subdivision
i. Based on set assumptions, we vectorially define the number of policyholders per merit class by year of enrollment and number of years elapsed. Thus calculating the distribution of class sizes for a year in which the system has reached a steady state.
ii. We calculate the class-size distribution for each risk level by introducing multiple risk levels for policyholders.
iii. We calculate insurance premiums based on a bonus-malus system and a flat-rate system, taking into consideration the premium increase/reduction rate for each class. In this way, we ascertain the characteristics of the bonus-malus system.
iv. We calculate the loss ratio for each merit class based on the distribution of policyholders at each risk level in each merit class.
We arrived at the following conclusions: i. Compared to a flat-rate system, a bonus-malus system is better able to reflect risk levels in insurance premiums.
ii. When rate classes are subdivided, the premium differential attributable to rate class between policyholders at the same risk level is less pronounced under a bonus-malus system than under a flat-rate system. But even bonus-malus systems cannot fully absorb all differences in policyholder risk levels.
iii. Based on this paper’s assumptions, we determined the relationship between premium increase/reduction rates and loss ratios for each merit class.
KEYWORDS: Bonus-malus system; rate class subdivision
Volume
Toyko
Year
1999
Categories
Actuarial Applications and Methodologies
Ratemaking
Classification Plans
Actuarial Applications and Methodologies
Ratemaking
Experience Rating
Business Areas
Automobile
Personal
Publications
ASTIN Colloquium
