= Exponential misspecification of shape-one-half gamma claims
{title2=$R<R_I=\rho/((1+\rho)\mu)$}
Replacing a shape-one-half gamma claim law by an <exponential distribution> with the same mean overestimates the <adjustment coefficient>. Indeed $R_I-R=\beta[3(1+\rho)-\sqrt{(\rho+9)(\rho+1)}]/[2(1+\rho)]>0$ because the difference of the squared terms is $8\rho(1+\rho)$. The resulting putative <Lundberg inequality> bound $e^{-R_Iu}$ is smaller than the valid true-model bound $e^{-Ru}$ for $u>0$; the former is not justified for the true claim law. The true variance is twice the assumed variance, and its exponential tail decays more slowly.
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