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

tel-00703797, version 2 - 7 Jun 2012
Chapitre 1. Sur la nécessité d’un modèle de marché
delta lapse rate (pts)
0 1 2 3 4
FC agent
PC agent
FC broker
TPL agent
PC broker
PC direct
TPL broker
FC direct
TPL direct
Customer behaviors
4 6 8 10 12
central lapse rates (%)
Figure 1.1: Comparison of distribution channels and cover types
the fact the brokers are paid to find the cheapest premium. The direct channel shows higher
central lapse rates ˆπn(1), but the estimated delta lapse rates are lower than those for Broker
channel. Direct channel are designed for customers shopping around on internet, so it seems
logical that their propency to lapse should be higher. We would have expected the same to
hold for delta lapse rates ∆1+(5%). The estimated delta rate of the direct channel might still
be underestimated. In addition to the absence of market proxies in the TPL direct database,
the direct channel is also small in size. Hence, higher uncertainty on those estimates might
explain low delta lapse rates for FC/PC direct subsets.
1.4.3 Backtesting
In this subsection, we present backtesting results for the fitted GLMs. We start by looking
only at an aggregate level: channel and coverage. The results are given in Table 1.11, reporting
observed and fitted lapse rates. The observed lapse rate rj for the jth group is computed as
the average lapse rate variable over the jth group, whereas fitted lapse rate is the average of
the fitted probabilities ˆπi over the jth group given the observed explanatory variables for each
individual 1
nj
nj
i=1 ˆπi.
The fitted results are good, since for each subgroup, the deviation is below one percentage
point. Compared to the previous backfit table, the improvements with rebate level, market
proxy and datasplit are amazing. The two subgroups for which we use market proxy, the
results are even better (deviation < 0.1pt), see TPL agent and direct. However, we must
recognize that observed price ratio are relatively small: for 85% of the portfolio, the difference
is below 5%. Hence, the model appropriately catches the lapse phenomenon when the variation
in premium remains reasonable.
To further assess the predictive power of our GLM fits, we focus on the TPL coverage
product. We consider three subpopulations representing three different behaviors: (i) old
drivers with at least two contracts in the household, (ii) working class with a decreasing
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