Solution
= Solution
With $a=0$ and $b>0$, the recurrence is $p_n=(b/n)p_{n-1}$. Iteration gives $p_n=p_0b^n/n!$. Since $\sum_{n\ge0}b^n/n!=e^b$, normalization gives
$$
\boxed{N\sim\operatorname{Poisson}(b),\qquad p_n=e^{-b}\frac{b^n}{n!}.}
$$
Hence the <claim count distribution> is a <Poisson distribution> of mean $b$, and the <Panjer recursion> begins at $g_0=e^{-b}$.