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
Another way to select significant explanatory variables is to use the analysis of deviance.
It consists in looking at the difference of deviance ln L between two models, i.e. ratios of
likelihood. Using an asymptotic distribution, either chi-square or Fisher-Snedecor distributions,
a p-value can be used to remove or to keep an explanatory variable. Based on this fact,
statistical softwares generally provide a function for the backward and the forward selection
using an automatic deviance analysis
In conclusion, GLM is a well-known statistical method in actuarial science. This fact
motivates its use to model lapse rate. Since it is a classic among statistical models, fitting
method and variable selection use state-of-art algorithms providing robust estimator. So, there
is absolutely no problem in applying GLMs for a daily use. In the following section, we apply
GLMs to explain the customer price-sensitivity.
1.3 Simplistic applications and biased business conclusions
This section is intended to present quite naive GLM applications and to show how they
can lead to inconclusive or even biased findings. First, we use a dataset with poor and limited
data, and then a larger dataset with more comprehensive data. Finally, we summarize the
issues encountered. It may seem obvious, but to study customer price-sensitivity, insurers
need to collect the premium proposed to customers when renewing policy, especially for those
who lapse.
For confidential reasons, the country names are not revealed, but we study two continental
European insurance markets. In this part of the world, the insurance penetration rate is
considered high, e.g., 8.6% in France, 7% in Germany, 7.6% in Italy, according to Cummins
and Venard (2007). Thus, the insurance markets studied are mature as well as competition
level is intense. Furthermore, data outputs presented in this paper have been perturbed, but
original conclusions have been preserved.
1.3.1 An example of poor data
In this subsection, we work with a (representative) subset of a 1-year lapse history database
in 2003. Each line of the dataset represents a policy for a given vehicle. The dataset suffers a
major problem because only few variables are available.
Descriptive analysis
To better understand interactions between lapses, the premium and other explanatory
variables, we start with a short descriptive analysis. As a general comment, all variables in
the dataset are dependent to the lapse variable according to a Chi-square test. At our disposal,
we have the last year premium and the proposed premium. Computing the premium ratio,
we observe that most of the portfolio experienced a price decrease, probably due to the ageing
and the market conditions. We expect to slightly underestimate the true price sensitivity of
clients, since customers attention will be released.
Turning to customer variables, we focus on gender and driver age variables, reported in
Table 1.2. As the age of the customer increases, the lapse rate decreases. So, the most sensitive
clients seem to be the youngest clients. The gender ∗ does not have any particular impact of
∗. In a near future, insurers will no longer have the right to discreminate premium against the gender of
the policyholder according to the directive 2004/113/CE from the European comission.
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