= Cramér–Lundberg ruin asymptotic
{c}
{title2=$e^{Ru}\psi(u)\to \rho/(R\int xe^{Rx}f_I(x)\,dx)$}
In the <classical risk model> with positive <relative safety loading> $\rho$ and <adjustment coefficient> $R$, tilting the ruin <defective renewal equation> gives a proper <renewal equation>. The <key renewal theorem> yields $e^{Ru}\psi(u)\to \rho/[R\int_0^\infty xe^{Rx}f_I(x)\,dx]$. The constant is positive if the denominator is finite and zero if it is infinite; the claim-size density provides the nonarithmetic hypothesis.
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