Aggregate claims model
= Aggregate claims model
{title2=$S=\sum_{j=1}^N X_j$}
An aggregate claims model separates the number $N$ of claims from their sizes $X_j$, with total $S=\sum_{j=1}^N X_j$ and the empty sum equal to zero. Under <independent and identically distributed random variables> for claim sizes, independent of $N$, <conditional expectation> gives tractable moments and transforms.