ECOMOR and LCR reinsurance with gamma-like claims

•We study the asymptotic tail behaviour of the reinsured amounts for ECOMOR and LCR.•The case of gamma-like claims is considered.•Precise asymptotic formulae and tight asymptotic bounds are obtained for both treaties.•The tails of two treaties have the same decay rate as that of the sums of i.i.d. claims.

Assuming that the claim sizes of an insurance company have a common distribution with gamma-like tail, we study the asymptotic tail behaviour of the reinsured amounts under the ECOMOR and LCR reinsurance treaties, respectively. Our novel results include a precise asymptotic expansion for the tail probability of the reinsured amounts under the ECOMOR treaty and tight asymptotic bounds for the LCR case. As a by-product we derive a precise asymptotic expansion for the tail of the product of independent regularly varying random variables.