SOA Exam ASTAM Spring 2026, Question 2
Study guide: Exam ASTAM
NED Insurance Company sells a liability insurance policy. The policyholder can select a deductible of 0, 500, or 1000.
You have the following data from 2024.
| Ground-Up Loss | Count | Total Ground-Up Losses |
|---|---|---|
| 0-500 | 770 | 172,000 |
| 500-1000 | 450 | 328,000 |
| 1000-2000 | 520 | 748,000 |
| 2000-4000 | 450 | 1,276,000 |
| 4000-6000 | 140 | 687,000 |
| 6000+ | 170 | 1,914,000 |
| Total | 2,500 | 5,125,000 |
Part a (2 points)
(i) Calculate the expected payment per loss.
(ii) Calculate the expected insurance payment per loss with a deductible of 500.
(iii) Calculate the expected insurance payment per loss with a deductible of 1000.
Part b (1 point)
NED develops their base rate using a deductible of 500.
(i) Determine the indicated deductible relativity for a zero deductible policy.
(ii) Determine the indicated deductible relativity for a policy with a deductible of 1000.
Part c (2 points)
NED is concerned about the tail risk for this portfolio.
(i) Calculate the mean excess loss of the ground-up losses for a threshold of x = 6000.
(ii) State with reasons the implications of this result with respect to the tail of this distribution.
Part d (3 points)
NED has requested a reinsurance company quote the cost of two different reinsurance contracts for this policy. The coverages are:
- Contract A: excess of loss insurance with retention of 4000; that is, for each loss the reinsurer will pay any excess of the ground-up loss over 4000.
- Contract B: pays 50% of the excess of the ground-up loss over 2000, with a maximum reinsurance payment of 2000.
(i) Calculate the reinsurer's expected cost per loss for each of these reinsurance contracts.
(ii) NED is primarily concerned about tail risk for this policy. State with reasons which of these two reinsurance coverages is more appropriate.
Part e (1 point)
NED is considering offering a policy with no deductible but with an upper limit of 6000. Describe one advantage and one disadvantage to the insurer of offering this policy, compared with a policy with no upper limit and with a 1000 deductible.
Answer this question and see the worked solution