## Definition ==Coinsurance== is a provision under which the insurer pays a fixed percentage $c$ (where $0 < c \leq 1$) of the covered loss, with the policyholder responsible for the remaining fraction $1 - c$. Applied after the deductible, the insurer's payment is: $ \text{Payment} = c \cdot (X - d)^+ $ > [!example]- A policy has a $\$200$ deductible and 70% coinsurance. If the loss is $\$1{,}200$, how much does the insurer pay? > $ \text{Payment} = 0.70 \times (1200 - 200) = 0.70 \times 1000 = \$700 $ > The policyholder pays the remaining $\$200 + \$300 = \$500$.