 Limited excess of loss reinsurance

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 $\mathbb{P}(X>M)$.