Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

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Actuarial Modelling of Claim Counts
models and high-dimensional data. The book may also serve as a textbook at graduate level
further to an introduction to basic principles explained in simple models.
The opening Chapters 1 and 2 present basic notions of risk and risk characteristics and
their theoretical representation in stochastic models with fixed and random effects and more
or less specified classes of distributions. Anticipating the orientation of the book, emphasis is
placed on parametric models for the number of claims. This gives clarity to the exposition and
also sets a suitable framework for discussion of model choice and model calibration that goes
way beyond what is usually found in conventional tutorials. Poisson conditional distributions
with varying exposures are merged with different mixing distributions on the individual
proportional hazards, and there are extensions to generalized linear (regression) models, time
trends, and spatial patterns. Statistical calibration is carried out with maximum likelihood
methods but also with alternative schemes like generalized estimating functions. Ample
numerical examples with authentic data gives real life to the theoretical ideas throughout.
Claim counts remain a main theme, but the remainder of the book nevertheless presents
a wealth of material, partly based on recent research by the authors: credibility theory,
Bayes estimation with exponential loss, bonus-malus systems in a number of variations,
elements of heavy-tailed distributions, bonus hunger and other ‘behavioural’ problems related
to individual experience rating, optimal design of bonus-malus systems for aggregates of
sub-portfolios, and much more. The final chapter is devoted to a carefully conducted case
study of the French bonus-malus system.
I would like to thank the authors for soliciting my views on a draft version of the book and
for inviting my preface to their work. Most of all I would like to thank them for undertaking
the formidable task of collecting and making accessible to a wide readership an area of
actuarial science that has undergone great changes over the past few decades while remaining
essential to decision making in insurance.
Ragnar Norberg
London, March 2007