= Leading exponential term determines a ruin adjustment coefficient
{title2=$\psi(u)\sim a e^{-ru},\quad a>0\ \Longrightarrow\ R=r,\ A=a$}
If the <Cramér–Lundberg ruin asymptotic> has a finite positive constant, compare it with the leading nonzero term of a finite exponential representation. An <adjustment coefficient> smaller than that term's decay rate would give limit zero; a larger coefficient would give infinity. Thus the two rates agree and the prefactor is the leading coefficient. Terms with zero coefficient are absent and do not determine a decay rate.
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