SOA Exam ASTAM Spring 2023, Question 1

Study guide: Exam ASTAM

You are the actuary for an insurance company that writes one year insurance coverage on a risk with the following frequency and severity distributions.

Number of Losses	Probability
0	0.20
1	0.25
2	0.40
3	0.15

Amount of Loss	Probability
100	0.50
200	0.40
500	0.10

Let $S$ denote the aggregate losses in a year for this risk.

Part a (2 points)

Calculate the probability that $S \le 350$ .

Part b (1 point)

For each policy, the premium is set at 1.15 times the expected annual claim payments.

Calculate the premium for a policy with no policy modifications.

Part c (2 points)

Show that the premium for a policy with an ordinary deductible of 100 per loss is 140 to the nearest 10. You should calculate the premium to the nearest 1.

Part d (3 points)

Calculate the premium for a policy with an aggregate deductible of 100 per insured for each year.

Part e (4 points)

The insurer plans to buy stop-loss reinsurance for a policy which has no coverage modifications.

(i) (3 points) Calculate the expected annual reinsurance payment with a stop-loss deductible of 1000.
(ii) (1 point) Explain why the insurer would prefer to use stop-loss coverage rather than setting a policy limit of 1000.

Answer this question and see the worked solution