Short-Term Insurance and Reinsurance Coverages

Write what the insurer pays for each loss before you take any expected value. With a deductible d and a limit u it is E[X ∧ u] − E[X ∧ d]; per payment, divide by S(d).

A lesson for this topic

Question 1

Losses follow a Pareto distribution with $\alpha = 3$ and $\theta = 2{,}000$ . An insurance policy has an ordinary deductible of 500.

Calculate the expected payment per loss.

Question 2

Losses follow a Pareto distribution with $\alpha = 2$ and $\theta = 1{,}500$ . A policy has an ordinary deductible of 500 and a maximum covered loss of 5,000.

Calculate the expected payment per payment.

Question 3

Losses follow an exponential distribution with mean 1,000. A policy has an ordinary deductible of 250 and a maximum covered loss of 2,250.

Calculate the expected payment per payment.

Question 4

Losses follow an exponential distribution with mean 2,000. A policy has a franchise deductible of 500: it pays nothing on a loss of 500 or less, and pays the full loss when the loss exceeds 500.

Calculate the expected payment per loss.

Question 5

Losses are uniformly distributed on $(0, 2{,}000)$ . A policy has a franchise deductible of 400 and a maximum covered loss of 1,500: when the loss exceeds 400, it pays the loss up to 1,500.

Calculate the expected payment per payment.