  We investigate the probability that an insurance portfolio gets ruined within
a finite time period under the assumption that the r largest claims are
(partly) reinsured. We show that for regularly varying claim sizes the
probability of ruin after reinsurance is also regularly varying in terms of the
initial capital, and derive an explicit asymptotic expression for the latter.
We establish this result by leveraging recent developments on sample-path large
deviations for heavy tails. Our results allow, on the asymptotic level, for an
explicit comparison between two well-known large-claim reinsurance contracts,
namely LCR and ECOMOR. We finally assess the accuracy of the resulting
approximations using state-of-the-art rare event simulation techniques.
