Actuarial Notes

SOA Exam ASTAM Fall 2025, Question 4

Study guide: Exam ASTAM

For a health insurance policy, the number of losses in a year is distributed as a Poisson distribution with an expected number of losses equal to 1.

The ground-up loss severity distribution is given in the following table:

Amount Probability
100 0.6
500 0.3
1000 0.1

Number of losses and loss severity are independent.

Part a (3 points)

(i) Calculate the Loss Elimination Ratio (LER) with an ordinary deductible of 60.

(ii) Calculate the insurer's expected payment per loss with an ordinary deductible of 60.

(iii) Calculate the ordinary deductible that would be necessary to achieve a LER of 40%.

Part b (2 points)

(i) Describe the difference between an ordinary deductible and a franchise deductible.

(ii) Describe a type of insurance which might typically use a franchise deductible.

Part c (4 points)

The insurer decides to impose an ordinary deductible on each claim that is the greater of 20% of the loss or 100. Let S denote the aggregate claims paid after the deductible for each policy.

(i) Show that \Pr[S = 0] is 0.67 to the nearest 0.01. You should calculate the value to the nearest 0.0001.

(ii) Using the recursive method, calculate \Pr[S < 1000]. (Hint: Work in units of 400.)

Part d (2 points)

The insurer purchases stop-loss insurance with an aggregate deductible of 1000, based on claims paid by the insurer. Calculate the net premium for this coverage.

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Concepts tested

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