= Claims inflation of a fixed reinsurance layer
{title2=$\mathbb E[L_{M,A}(hX)\mid hX>M]=hC(\mu,\sigma;M/h,A/h)$}
For positive inflation factor $h$, $L_{M,A}(hX)=hL_{M/h,A/h}(X)$. The conditioning event also changes to $X>M/h$. If claims have a <lognormal distribution>, the same result follows by replacing their log-mean $\mu$ by $\mu+\log h$ and keeping the contractual attachment and limit fixed. Merely multiplying the original conditional mean by $h$ would hold those effective thresholds incorrectly fixed.
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