## Definition A ==Benefit Limit== (or policy limit) is the maximum amount an insurer will pay for a covered loss. If the computed payment exceeds the limit $u$, the insurer pays only $u$. With a deductible $d$ and coinsurance $c$: $ \text{Payment} = \min\!\big(c \cdot (X - d)^+,\ u\big) $ > [!example]- A policy has a $\$500$ deductible, 100% coinsurance, and a $\$10{,}000$ benefit limit. What does the insurer pay on a $\$15{,}000$ loss? > After deductible: $15{,}000 - 500 = 14{,}500$. > Apply limit: $\min(14{,}500,\ 10{,}000) = 10{,}000$. > The insurer pays $\$10{,}000$ and the policyholder bears the remaining $\$5{,}000$ (plus the $\$500$ deductible).