id: 05220290
dt: j
an: 2011a.00862
au: Lescourret, Laurence; Robert, Christian Y.
ti: Extreme dependence of multivariate catastrophic losses.
so: Scand. Actuar. J. 2006, No. 4, 203-225 (2006).
py: 2006
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: K80 K90
ut: extreme dependence; multivariate catastrophic losses; heavy-tailed
distributions; probability of catastrophic events
ci:
li: doi:10.1080/03461230600889645
ab: This paper deals with modelling of the dependence in insurance loss
severities caused by natural catastrophes in several different lines of
business. The authors introduce a common factor for modelling extreme
dependence. The basic idea of the factor approach is to use a single
intensity variable to describe aggregate amounts of losses across
different lines of business. Let us denote by $X\sb{i,j}$ the amount of
losses of the $j$-th line of business for the $i$-th natural disaster.
It is considered the following model
$X\sb{i,j}=T\sb{j}(Y\sb{i}η\sb{i,j}), j=1,2$, where $Y\sb{i}$ is the
intensity of the $i$-th natural disaster and is a common latent factor,
the $η\sb{i,j}$ are so-called multiplicative disturbances which are
independent of $Y\sb{i}$, and the $T\sb{j}$ are transformation
functions. The authors consider the models with multivariate
distributions where the marginals are Pareto-type. Bivariate extreme
value theory is presented and it is derived from the factor model a
class bivariate extreme value distributions which takes into account
the dependence structure of catastrophic losses. Several examples are
presented. The authors discuss two common approaches of estimating
bivariate extreme value distribution and introduce an estimator adapted
to proposed factor model. It is studies the finite sample behaviour of
the estimator on simulated data and it is compared its performance with
those of standard estimators. The application to storm insurance data
is presented.
rv: A. D. Borisenko (Kyïv)