A "simple approximation" of a ruin probability is an approximation using on
ly some moments of the claim distribution and not the detailed tail behavio
ur of that distribution. Such approximations may be based on limit theorems
or on more or less ad hoc arguments. The most successful simple approximat
ion is certainly the De Vylder approximation, which is based on the idea to
replace the risk process with a risk process with exponentially distribute
d claims such that the three first moments coincide. That approximation is
known to work extremely well for "kind" claim distributions. The main purpo
se of this paper is to analyse the De Vylder approximation and other simple
approximations from a more mathematical point of view and to give a possib
le explanation why the De Vylder approximation is so good. (C) 2000 Elsevie
r Science B.V. All rights reserved.