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

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Actuarial Modelling of Claim Counts
are available under most statistical packages to estimate the regression parameters by
maximum likelihood.
Pay-As-You-Drive System
Every kilometer travelled by a vehicle transfers risk to its insurer: the total cost of the
coverage thus increases kilometer by kilometer. This is why several authors, including
Butler (1993) suggested charging a cents-per-kilometer based premium; the car-kilometer
should be adopted as the exposure unit instead of the car-year that is currently used. Motor
insurance companies are adopting a new scheme called ‘pay as you drive’ (henceforth
referred to as PAYD for the sake of brevity). Under a PAYD system, a driver pays for every
kilometer driven at a rate varying from a premium to use the busiest roads at peak hours to
a lower rate for the rural roads.
Several insurance companies (including the pioneering company Norwich Union,
http://www.norwichunion.com/pay-as-you-drive/) have now started to offer a motor
insurance policy under a PAYD system after successful pilot schemes involving thousands of
motorists. With PAYD systems, drivers are provided with in-car Global Positioning System
(GPS) devices coupled with maps, enabling the insurance company to calculate insurance
premiums for each journey, depending on time of day, type of road and distance travelled.
A ‘black box’ is installed in the car and receives signals from GPS technology to determine
the vehicle’s current position, speed, and time and direction driven. The black box then
acts as a wireless modem to transmit these inputs through standard mobile phone networks
to the insurer. The insurer sends a monthly bill to the customer based on vehicle usage,
including time of day, type of road and distance travelled. Historical data then provide
detailed information of how, when and where cars are actually used, and whether accidents
and claims can be identified with particular factors. Moreover, the tracker detects speed
infringements and more generally, the aggressiveness behind the wheel. Dangerous driving
habits could lead to higher premiums for car insurance, increasing road safety. In addition
to the static measures of risk, such as the driver’s age, dynamic measures, such as speed,
time of day, and location, are used to give the best possible overall risk assessment.
The generalization of the PAYD system is also expected to change motorists’ attitudes:
like petrol, insurance is bought on a pay-as-you-drive basis, and people think of their
insurance costs as related to their actual use of their vehicle. Several North-American studies
demonstrate that PAYD systems could reduce motoring by more than 10 %. The PAYD
rating system is expected to decrease congestion and pollution (since the busier roads usually
attract the higher rates).
Experience Rating
The trend towards more classification factors has lead the supervising authorities to exclude
from the tariff structure certain risk factors, even though they may be significantly correlated
to losses. Many states consider banning classification based on items that are beyond the
control of the insured, such as gender or age. The resulting inadequacies of the a priori
rating system can be corrected for by using the past number of claims to reevaluate future
premiums. This is much in line with the concept of fairness: as it will be seen from Chapter 2,
a priori ratemaking penalizes individuals who ‘look like’ bad drivers (even if they are in