Exponential tilt of the ruin renewal kernel
= Exponential tilt of the ruin renewal kernel
{title2=$k_R(x)=(\lambda/c)e^{Rx}\overline F(x)$}
The <ultimate ruin probability> satisfies a tail-forced <defective renewal equation>. Multiplying it by $e^{Ru}$ at an <adjustment coefficient> turns its kernel into the probability density $k_R$. Normalization is exactly $\lambda(M(R)-1)=cR$. The density is absolutely continuous even when the original claim law has atoms; thus it has a <nonarithmetic distribution>.