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

Risk Classification 65
2.3.4 Multiplicative Tariff
When the a priori variables x ij s are coded by means of binary variables (so that each
policyholder is represented by a vector of 0s and 1s), the intercept 0 represents the risk
associated to the reference class. Then, the annual claim frequency i associated with
characteristics x i is of the following multiplicative form
i = exp 0 ∏
exp j
jx ij =1
where exp 0 is the annual claim frequency corresponding to the reference class and
exp j models the impact of the jth ratemaking variable. The intercept 0 represents the risk
associated with the reference class. If j > 0, being in the class coded by the jth explanatory
variable increases the score and thus the annual claim frequency. Conversely, if j < 0, the
score and the annual claim frequency decrease when x ij = 1. With the exponential link, high
(respectively low) scores mean high (respectively low) claim frequencies. The following
example makes this clear.
Example 2.4
of the form
Here,
Let us continue Example 2.2. In Portfolio A, the score for policyholder i is
score i = 0 + 1 x i1 + 2 x i2 +···+ 7 x i7
etc
exp 0 = annual claim frequency for men aged 31–60, living in an
urban area, paying the premium once a year, using the
car for private purposes
exp 0 + 1 = annual claim frequency for men less than 24, living in an
urban area, paying the premium once a year, using the
car for private purposes
exp 0 + 2 = annual claim frequency for men aged 25–30, living in an
urban area, paying the premium once a year, using the
car for private purposes
exp 0 + 3 = annual claim frequency for men over 60, living in an
urban area, paying the premium once a year, using the
car for private purposes
exp 0 + 4 = annual claim frequency for women aged 31–60, living in an
urban area, paying the premium once a year, using the
car for private purposes