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
Generalized Linear Models are widely known and respected methods in non-life insurance.
However, they have some inherent constraints with GLMs. Thus, in Section 1.6, we test
Generalized Additive Models, which allow for non linear terms in the predictor. Like GLMs,
the quality of the findings attained is directly related to the data provided. Using limited
variables will produce approximate results, whereas, dealing with an extensive set of variables
lead to proven results.
Applying GAMs, despite their additional complexity, can be justified in cases where GLMs
fail to provide realistic lapse predictions and we have substantial datasets. Note that GAMs
can model interactions between explanatory variables. Not restricted to linear terms, they
consequently provide us with a more adaptive tool. Caution should however be exercised, as
they may overfit the data when applied to limited datasets. This could then imply business
inconsistency.
In this paper, we have explored the price elasticity topic from various viewpoints. Once
again, our research has further demonstrated that the quality of data used in actuarial studies
unequivocally affects the findings reached. In addition, the key role of the market proxies
in estimating price sensitivity has been established. Market competition modelling, see, e.g.,
Demgne (2010), Dutang et al. (2012), is therefore relevant.
The conclusions drawn from customer price sensitivity studies should in any respect be
weighed carefully. Charging higher premiums to loyal customers could seem unfair in light of
the fact that those same customers usually have a better claims history. By the same token,
relying on the market context with its inherent uncertainty to predict price sensitivity could
be misleading. In summary, insurers must have a well informed overview of the market, the
customer base, and a keen awareness of the pros and cons of potential pricing adjustments.
The models presented herein serve as decision-making support tools and reinforce business
acumen.
1.8 Appendix
1.8.1 Generalized linear and additive models
Univariate exponential family
Clark and Thayer (2004) defines the exponential family by the following density or mass
probability function
f(x) = e d(θ)e(x)+g(θ)+h(x) ,
where d, e, g and h are known functions and θ the vector of paremeters. Let us note that the
support of the distribution can be R or R+ or N. This form for the exponential family is called
the natural form. When we deal with generalized linear models, we use the natural form of
the exponential family, which is
f(x, θ, φ) = e θx−b(θ)
a(φ) +c(x,φ) ,
where a, b, c are known functions and θ, φ ∗ denote the parameters. This form is derived
from the previous by setting d(θ) = θ, e(x) = x and adding a dispersion parameter φ. The
exponential family of distributions in fact contains the most frequently used distributions.
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∗. the canonic and the dispersion parameters.