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

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Actuarial Modelling of Claim Counts
Even in a pure no-fault motor environment, the police still ask which driver was at fault (or
the degrees to which the drivers shared the fault) because at-fault events cause the insurance
premium to rise at the next policy renewal.
Insurance Ratemaking
Cost-based pricing of individual risks is a key actuarial ratemaking principle. The price
charged to policyholders is an estimate of the future costs related to the insurance coverage.
The pure premium approach defines the price of an insurance policy as the ratio of the
estimated costs of all future claims against the coverage provided by the insurance policy
while it is in effect to the risk exposure, plus expenses.
The property/casualty ratemaking is based on a claim frequency distribution and a loss
distribution. The claim frequency is defined as the number of incurred claims per unit
of earned exposure. The exposure is measured in car-year for motor third party liability
insurance (the rate manual lists rates per car-year). The average loss severity is the average
payment per incurred claim. Under mild conditions, the pure premium is then the product
of the average claim frequency times the average loss severity. The loss models for motor
insurance are reviewed in Chapters 1–2 (frequency part) and 5 (claim amounts).
In liability insurance, the settlement of larger claims often requires several years. Much of
the data available for the recent accident years will therefore be incomplete, in the sense that
the final claim cost will not be known. In this case, loss development factors can be used to
obtain a final cost estimate. The average loss severity is then based on incurred loss data. In
contrast to paid loss data (that are purely objective, representing the actual payments made
by the company), incurred loss data include subjective reserve estimates. The actuary has to
carefully analyse the large claims since they represent a considerable share of the insurer’s
yearly expenses. This issue will be discussed in Chapter 5, where incurred loss data will be
analysed and appropriately modelled.
Risk Classification
Nowadays, it has become extremely difficult for insurance companies to maintain cross
subsidies between different risk categories in a competitive market. If, for instance, females
are proved to cause significantly fewer accidents than males and if a company disregarded
this variable and charged an average premium to all policyholders regardless of gender, most
of its female policyholders would be tempted to move to another company offering better
rates to female drivers. The former company is then left with a disproportionate number of
male policyholders and insufficient premium income to pay for the claims.
To avoid lapses in a competitive market, actuaries have to design a tariff structure that
will fairly distribute the burden of claims among policyholders. The policies are partitioned
into classes with all policyholders belonging to the same class paying the same premium.
Each time a competitor uses an additional rating factor, the actuary has to refine the partition
to avoid losing the best drivers with respect to this factor. This explains why so many factors
are used by insurance companies: this is not required by actuarial theory, but instead by
competition among insurers.
In a free market, insurance companies need to use a rating structure that matches the
premiums for the risks as closely as possible, or at least as closely as the rating structures used