What is this operation on random variables called? Let $X$ be a random variable and let $N$ be a discrete random variable which takes values in the non-negative integers. Let $X_1, X_2, ...$ be a sequence of i.i.d. random variables with the same distribution as $X$, all of which are also independent of $N$. Is there a name for the random variable
$$Y = X_1 + X_2 + ... + X_N?$$
The only hint I've found is that this appears to be what actuaries call the aggregate risk model. One reason I ask is that there is a very nice expression for the cumulant generating function $C_Y$ of $Y$ in terms of the cumulant generating functions $C_X, C_N$ of $X, N$, namely
$$C_Y = C_N \circ C_X.$$

It is called compound random variable. Please check:
http://en.wikipedia.org/wiki/Panjer_recursion
