Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Short-Term Insurance and Reinsurance Coverages Practice Questions
Short-term insurance coverages on SOA Exam FAM cover property and casualty policy forms, deductibles, coinsurance, and reinsurance structures. This topic introduces how insurers transfer and manage underwriting risk.
72 questions27 easy28 medium17 hard2026 syllabus
Sample Questions
Question 1
Easy
Losses follow an exponential distribution with mean 800. Calculate the mean excess loss at d=300.
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Correct Answer: D
Solution
D is correct.
The exponential distribution is memoryless: e(d)=E[X−d∣X>d]=θ for all d≥0. With θ=800, e(300)=800.
Question 2
Medium
An excess-of-loss reinsurance treaty has a retention of 50,000. A loss of 80,000 occurs. How much does the reinsurer pay?
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Correct Answer: B
Solution
B is correct.
Under excess-of-loss reinsurance with retention M=50,000, the reinsurer pays max(X−M,0)=max(80,000−50,000,0)=30,000.
Question 3
Hard
Losses follow a Pareto distribution with α=3 and θ=2,000. Calculate the loss elimination ratio (LER) for an ordinary deductible of d=500.
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Correct Answer: D
Solution
D is correct.
For a Pareto distribution with α=3 and θ=2,000:
E[X]=α−1θ=22,000=1,000.
The limited expected value at d=500: E[X∧d]=α−1θ[1−(θ+dθ)α−1]=1,000[1−(0.8)2]=1,000×0.36=360 LER=E[X]E[X∧d]=1,000360=0.3600
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