## Definition A ==Deductible== is the initial amount of a loss that the policyholder must pay before the insurance coverage begins. If the loss $X$ is less than or equal to the deductible $d$, the insurer pays nothing. The amount subject to insurance after a deductible is: $ (X - d)^+ = \max(X - d,\ 0) $ > [!example]- Under a policy with a $\$500$ deductible, what does the insurer pay on losses of $\$300$ and $\$2{,}000$? > - For a $\$300$ loss: $(300 - 500)^+ = 0$. The insurer pays nothing. > - For a $\$2{,}000$ loss: $(2000 - 500)^+ = 1{,}500$. The insurer pays $\$1{,}500$.