  In this paper we discuss the asymptotic behaviour of random contractions
$X=RS$, where $R$, with distribution function $F$, is a positive random
variable independent of $S\in (0,1)$. Random contractions appear naturally in
insurance and finance. Our principal contribution is the derivation of the tail
asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an
extreme value distribution and the distribution function of $S$ satisfies a
regular variation property. We apply our result to derive the asymptotics of
the probability of ruin for a particular discrete-time risk model. Further we
quantify in our asymptotic setting the effect of the random scaling on the
Conditional Tail Expectations, risk aggregation, and derive the joint
asymptotic distribution of linear combinations of random contractions.
