Independent solution

How to solve this Loss Models question

Setup

Setup

The payment is zero below the deductible and otherwise equals the excess loss. A payment below 0.5 is therefore equivalent to a loss below the deductible plus 0.5.

Y=(X−C)+,FX(x)=x2(0<x<1)Y=(X-C)_+,\qquad F_X(x)=x^2\quad(0<x<1)

Model

Model

The loss cumulative distribution is the square of the loss amount on its support, so substitute the shifted threshold into that distribution.

Pr⁡(Y<0.5)=Pr⁡(X<C+0.5)=(C+0.5)2\Pr(Y<0.5)=\Pr(X<C+0.5)=(C+0.5)^2

Compute

Compute

Taking the positive square root gives a loss threshold of 0.8. Subtracting 0.5 leaves deductible 0.3.

(C+0.5)2=0.64,C=0.30(C+0.5)^2=0.64,\qquad C=0.30

Answer

Answer

The deductible is 0.3, selecting choice B.

0.3(B)\boxed{0.3\quad\text{(B)}}