Erlang shape-two ruin prefactor
= Erlang shape-two ruin prefactor
{c}
{title2=$A=\frac{(1-R)(3-2R)}{3-R}$}
For unit-rate <Erlang distribution> of shape two claims put $q=\lambda/c<1/2$. The <adjustment coefficient> satisfies $q(2-R)=(1-R)^2$, so $1-R=(q+\sqrt{q^2+4q})/2$. In the interior-adjustment prefactor $(1-2q)/(2q(1-R)^{-3}-1)$, substituting $q=(1-R)^2/(2-R)$ gives the displayed expression. It is positive for $0<R<1$ and tends to one as the loading tends to zero.