Etude des marchés d'assurance non-vie à l'aide d'équilibres de ...

tel-00703797, version 2 - 7 Jun 2012
1.3. Simplistic applications and biased business conclusions
∆1−(5%) ˆπn(1) ∆1+(5%)
All -0.745 14.714 0.772
Old drivers -0.324 9.44 0.333
Young pol., working male -0.585 15.208 0.601
Young drivers -1.166 19.784 1.211
Table 1.4: Central lapse rates (%) and deltas (pts)
In Table 1.4, we report the predicted lapse rates and deltas for the whole dataset (first
line) as well as for three subsets: old drivers, young policies and working male, young drivers.
This first result exhibits the wide range of behaviors among a portfolio: young vs. old drivers.
However, delta values seem unrealistic: a 5% premium increase will increase the lapse rate
only by 0.772 pts. Based only on such predictions, one will certainly not hesitate to increase
premium.
As this small dataset only provides the driver age, GLM outputs lead to inconclusive or
dubious results. The old versus young segmentation alone cannot in itself substantiate the
lapse reasons. We conclude that the number of explanatory variables are too few to get reliable
findings with GLMs, and probably with any statistical models.
1.3.2 A larger database
In this subsection, we study another dataset from a different country in continental Europe
in 2004. As for the other dataset, a record is a policy purchased by an individual, so an
individual may have different records for the different covers he bought.
Descriptive analysis
This dataset is very rich and contains much more variables than the previous set. The
full list is available in Appendix 1.8.2. In Table 1.5, we present some explanatory variables.
The dataset contains policies sold through different distribution channels, namely tied-agents,
brokers and direct platforms, cf. first line of Table 1.5. Obviously, the way we sell insurance
products plays a major role in the customer decision to renew or to lapse. The coverage types
(Full Comprehensive, Partial Comprehensive and Third-Part Liability) have a lesser influence
on the lapse according to the first table.
The dataset also contains some information on claim history, e.g. the bonus/malus or the
claim number. In Table 1.5, we present a dummy variable for the bonus evolution (compared
to last year). From this table, we observe that a non-stable bonus seems to increase the
customer propency to lapse. This could be explained by the fact that decreasing or increasing
bonus implies the biggest premium difference compared to last year premium, raising the
customer attention.
At this stage, the claim number does not seem to influence the lapse. The policy age has
the same impact as in the previous dataset (cf. Table 1.3). The older is the policy the lower
the customer lapses. However, the opposite effect is observed for the vehicle age compared to
previous dataset.
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