Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Severity, Frequency, and Aggregate Models Practice Questions
Severity, frequency, and aggregate loss models on SOA Exam FAM test parametric distributions (exponential, Pareto, lognormal), compound Poisson models, and the Panjer recursive method for computing aggregate loss probabilities.
152 questions76 easy51 medium25 hard2026 syllabus
Sample Questions
Question 1
Easy
Which of the following is a property of a coherent risk measure?
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Correct Answer: A
Solution
A is correct.
Subadditivity is one of the four axioms of coherent risk measures (monotonicity, positive homogeneity, translation invariance, subadditivity).
Question 2
Medium
Which of the following statements about TVaR is FALSE?
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Correct Answer: B
Solution
B is correct.
TVaR0=E[X], while VaR0 is the minimum possible value (often 0 for loss distributions). Since E[X] generally does not equal the minimum, the statement that TVaR at level p=0 equals VaR at level p=0 is false.
Question 3
Hard
Continuing from the Panjer recursion with Poisson λ=3, f1=0.6, f2=0.4, and g0=0.04979, g1=0.08962. Calculate g2=P(S=2).
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Correct Answer: E
Solution
E is correct.
For compound Poisson (a=0, b=λ=3), Panjer's recursion simplifies to: gs=sλj=1∑sj⋅fj⋅gs−j For s=2: g2=23[1⋅f1⋅g1+2⋅f2⋅g0]=1.5[0.6×0.08962+0.8×0.04979]=1.5[0.05377+0.03983]=1.5×0.09360=0.14041. Verification by direct calculation: P(S=2) requires either one claim of size 2 or two claims each of size 1. P(N=1)P(X=2)+P(N=2)[P(X=1)]2=3e−3(0.4)+29e−3(0.36)=0.04979×2.82=0.14041. Common errors: dropping the λ/s=1.5 leading factor and reporting the bracket sum 0.09360; using j=1 instead of j=2 on the size-2 term to get 0.11053; omitting the 2⋅f2⋅g0 term entirely for 0.08066; or applying the non-simplified formula incorrectly to get 0.07020, which is g2/2 rather than g2.
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