Question

An auto insurance policy has a deductible of 1 and a maximum claim payment of 5. Auto loss amounts follow an exponential distribution with mean 2. Calculate the expected claim payment made for an auto loss.

Answer 1

The distribution of the auto loss amount here is given as:

as mean is parameter reciprocal here.

X exp(0.5)

Total claim payment is modelled here as:

10 Y = {X-1 14 X <1 1<x< 5 X > 5

The expected claim amount is now computed here as:

E(Y) = [ (x – 15() dx + 5 f® f(x) de

E(Y) = 0.5ce-0.5r dr - 0.5e-0.52 do +5 0.5e-0.52 dc

E(Y) = |--1e-0.57 | + -0.57 dx + (e-25 – e-0.5) + 5e-0.545

E(Y) = -0.5 – 5e-25 – 2e-25 - -0.5) + (6e-2.5 - e-0.5)

E(Y) = 2e-0.5 - e-2.5 = 1.130976

Therefore the expected claim payment made for an auto loss here is given as: 1.130976