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
Observed Fitted Observed Fitted Observed Fitted
Full Comp. 7.361 7.124 10.167 10.468 12.958 12.881
Part. Comp. 8.123 8.084 9.971 10.09 11.258 11.193
TPL 8.579 8.569 10.867 11.042 11.153 11.171
Agent Broker Direct
Table 1.11: Central lapse rates (%) and deltas (pts)
bonus-malus and an old vehicle, (iii) young drivers. We expect the population 3 to be the
most price-sensitive.
Prop. Obs. Fit. Std.Err. Prop. Obs. Fit. Std.Err. Prop. Obs. Fit. Std.Err.
Pop. 1 13 4.98 5.16 0.22 5 7.99 8.24 0.49 3 6.98 8.187 0.65
Pop. 2 13 8.45 8.65 0.32 16 11.59 12.36 0.50 17 12.44 13.02 0.61
Pop. 3 10 10.01 9.91 0.42 14 13.25 12.45 0.62 13 14.91 14.184 0.74
Agent Broker Direct
Table 1.12: Lapse rates and proportions (%)
In Table 1.12, we report the backfit results for the three selected populations separating
each distribution channel. Each block presents the proportion of population i in the total
subset, the observed lapse rate for population i, the mean of fitted lapse rates and standard
deviations. As expected the difference between the three populations is high whatever the
channel. Population 1 can be tagged as a sluggish behavior, Population 2 a kind of medium
behavior, while Population 3 represents highly sensitive customers.
1.4.4 Market scenarios
Having a market variable in the database allows us to perform market scenarios. In this
subsection, we briefly present this topic particularly interesting for business line managers. We
perform two basic scenarios: a 5% increase of market premium and a 5% decrease of market
premium.
Insurer Insurer
-5% 0% +5% -5% 0% +5%
Market -5% 8.007 8.763 10.481 12.538 14.143 17.589
Market 0% 7.801 8.548 10.152 9.604 11.958 14.696
Market +5% 7.645 8.359 9.916 8.638 10.943 13.589
Agent Direct
Table 1.13: Market scenarios (%)
The results are summarized in Table 1.13. It is surprising to see how the tied-agent
customers react very slowly when premium fluctuates. In particular when market decrease of
5% and the proposed premium increases by 5%, then the lapse rate goes only from 8.548%
to 10.481%. While for the direct channel, the lapse rate rockets from 11.958% to 17.589%.
Actually for any difference in premium, the lapse rate fluctuates largely for the direct channel
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