Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

5
Efficiency and Bonus Hunger
5.1 Introduction
5.1.1 Pure Premium
In nonlife business, the pure premium is the expected cost of all the claims that the
policyholder will file during the coverage period (under the assumption of the Law of Large
Numbers, i.e. a large portfolio comprising independent and identically distributed risks).
The actuarial ratemaking is based on a claim frequency distribution and a loss distribution.
The average claim frequency is defined as the number of incurred claims per unit of earned
exposure (the exposure is usually measured in car-year for motor insurance). The average
loss severity is the average payment per incurred claim.
In this chapter, as well as in the next one, we need to consider the claim severities. Even if
the premium updates induced by bonus-malus systems only depend on the number of claims
at fault filed with the insurance company, the design of efficiency measures, as well as the
study of the bonus-hunger phenomenon (i.e. the tendency for the policyholder to self-defray
minor accidents to avoid premium surcharges), require an accurate modelling for the cost of
the claims. This topic is dealt with in Section 5.2.
5.1.2 Statistical Analysis of Claim Costs
The computation of the pure premium relies on a statistical model incorporating all the
available information about the risk. The technical tariff aims to evaluate as accurately as
possible the pure premium for each policyholder via regression techniques. It is well known
that market premiums may differ from those computed by actuaries. In that respect, the
overall market position of the company compared to its competitors with regard to growth
and pricing is crucial. This chapter is devoted to technical tariff only.
Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems
S. Pitrebois and J.-F. Walhin © 2007 John Wiley & Sons, Ltd
M. Denuit, X. Maréchal,