Limited excess of loss reinsurance
= Limited excess of loss reinsurance
{title2=$L_{M,A}(X)=\min\{(X-M)_+,A\}$}
A <reinsurance> layer with attachment $M$ and payment limit $A$ pays nothing below $M$, the excess between $M$ and $M+A$, and $A$ above that. Its expected recovery is $\int_M^{M+A}\mathbb P(X>x)\,dx$, by the <tail integral formula for moments>. For continuous claims, conditioning on penetration of the layer divides this expectation by $\mathbb P(X>M)$.