Capped claim moments
= Capped claim moments
{title2=$\mathbb E\min(X,M)^r=r\int_0^M x^{r-1}\mathbb P(X>x)\,dx$}
For a positive claim and $r>0$, the <tail integral formula for moments> gives the displayed expression. In particular the first moment is $\int_0^M\overline F(x)\,dx$ and the raw second moment is $2\int_0^M x\overline F(x)\,dx$. If the claim law has a density, capping adds an <atom of a measure> at $M$ with mass $\mathbb P(X\ge M)$.