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. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.

In the present paper the author gives net premium formulae for a generalized largest claims reinsurance cover. If the claim sizes are mutually independent and identically 3-parametric Pareto distributed and the number of claims has a Poisson, binomial or negative binomial distribution, formulae are given from which numerical values can easily be obtained. The results are based on identities for compounded order statistics.