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

tel-00703797, version 2 - 7 Jun 2012
1.4. Incorporating new variables in the regression
lapse rates ∆1+ are again surprisingly low around 1 pt. In Appendix 1.8.2, we also compare
the observed lapse rate by channel and coverage type against the fitted lapse rate, see Table
1.17. The results are unsatisfactory.
1.3.3 Issues
The price-sensitivity assessment appears to be difficult. Getting outputs is easy but having
reliable estimates is harder. We are not confident on the lapse prediction as well as the
additional lapse rates ∆1+. A first answer is shown in Table 1.18 of Appendix 1.8.2, where we
present the predicted results when the dataset is split according to the distribution channel
or the coverage type. This split provides more realistic lapse rates, each fit better catches the
specificity of the distribution channel. Thus we choose to fit nine regressions in the following
in order to catch the full characteristics of the distribution channel and the coverage type.
However, this section reveals major issues of a rapid and simplistic application of GLMs.
We miss something as it does not really make sense that a 5% premium increase on the whole
portfolio leads to a lapse rate increase less than 1pt. In such situation, the insurer has all
reasons to increase premium by 5% and to get a higher gross written premium. The market
competition level drives the level of customer price-sensitivity that we can estimate. Therefore,
high cautions is needed when using GLMs predictions with few variables.
1.4 Incorporating new variables in the regression
This section focuses on identifying new key variables needed in the GLM regression in
order to get more reliable results. Attentive readers have probably noticed that some variables
have been forgotten in this first analysis. As we will see, they have a major impact on the
GLM outputs. Furthermore, taking into account previous conclusions on the large dataset of
Subsection 1.3.2, all results presented in this section are obtained by nine different regressions,
one for each channel and each coverage type.
1.4.1 Rebate levels
Firstly, we add to all regressions the rebate level variable, specifying the amount of rebate
granted by the agent, the broker or the client manager to the customer. As reported in Table
1.7, the number of customers having rebates is considerably high. The broker channel grants
a rebate to a majority of customers. Then comes the tied-agent channel and finally the direct
channel.
Full Comp. Part. Comp. TPL
Agent 56.62 36.84 22.26
Broker 62.25 52.5 36.24
Direct 23.05 22.89 10.37
Table 1.7: Proportion of granted rebates (%)
It seems logical that the direct channel does not grant rebates since the premium is generally
lower through the direct channel than with other distribution channels. The influence
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