Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Short-Term Insurance and Reinsurance Coverages Practice Questions

The exponential distribution is memoryless: $e(d) = E[X - d \mid X > d] = \theta$ for all $d \ge 0$. With $\theta = 800$, $e(300) = 800$.

(A) 300 is the deductible. (B) 500 subtracts the deductible from the mean. (D) 1,100 adds the deductible and mean. (E) 1,600 doubles the mean.

B is correct. Under excess-of-loss reinsurance with retention $M = 50{,}000$, the reinsurer pays $\max(X - M, 0) = \max(80{,}000 - 50{,}000, 0) = 30{,}000$.
Choice A is incorrect because 50,000 is the retention, the amount the insurer keeps, not what the reinsurer pays.
Choice C is incorrect because 80,000 is the total loss; the reinsurer does not pay the full amount.
Choice D is incorrect because 20,000 results from subtracting incorrectly.
Choice E is incorrect because the loss exceeds the retention, so the reinsurer does pay.

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