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.