Reinsurance under the LCR and ECOMOR Treaties with Emphasis on Light-tailed Claims

Suppose that, over a fixed time interval of interest, an insurance portfolio generates a random number of independent and identically distributed claims. Under the LCR treaty the reinsurance covers the first l largest claims, while under the ECOMOR treaty it covers the first l − 1 largest claims in excess of the lth largest one. Assuming that the claim sizes follow an exponential distribution or a distribution with a convolutionequivalent tail, we derive some precise asymptotic estimates for the tail probabilities of the reinsured amounts under both treaties.