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Summary: International Journal of Statistics and Management System, 2010, Vol. 5, No. 12, pp. 2158.
c 2010 Serials Publications
Estimation effects on stop-loss premiums
under dependence
Willem Albers
and Wilbert C.M. Kallenberg
Abstract
Even a small amount of dependence in large insurance portfolios can lead to huge
errors in relevant risk measures, such as stop-loss premiums. This has been shown in
a model where the majority consists of ordinary claims and a small fraction of special
claims. The special claims are dependent in the sense that a whole group is exposed
to damage. In this model, the parameters have to be estimated. The effect of the
estimation step is studied here. The estimation error is dominated by the part of
the parameters related to the special claims, because by their nature we do not have
many observations of them. Although the estimation error in this way is restricted
to a few parameters, it turns out that it may be quite substantial. Upper and lower
confidence bounds are given for the stop-loss premium, thus protecting against the
estimation effect.
1 Introduction. A well-known risk measure for large insurance portfolios is the so
called stop-loss premium E(S - a)+
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