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 Questions
76 Easy
51 Medium
25 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
Which of the following is a property of a coherent risk measure?
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?
Solution
B is correct.

TVaR0=E[X]\text{TVaR}_0 = E[X], while VaR0\text{VaR}_0 is the minimum possible value (often 0 for loss distributions). Since E[X]E[X] generally does not equal the minimum, the statement that TVaR at level p=0p = 0 equals VaR at level p=0p = 0 is false.
Question 3 Hard
Continuing from the Panjer recursion with Poisson λ=3\lambda = 3, f1=0.6f_1 = 0.6, f2=0.4f_2 = 0.4, and g0=0.04979g_0 = 0.04979, g1=0.08962g_1 = 0.08962. Calculate g2=P(S=2)g_2 = P(S = 2).
Solution
E is correct.

For compound Poisson (a=0a = 0, b=λ=3b = \lambda = 3), Panjer's recursion simplifies to: gs=λs∑j=1sj⋅fj⋅gs−jg_s = \frac{\lambda}{s}\sum_{j=1}^{s} j \cdot f_j \cdot g_{s-j} For s=2s = 2: g2=32[1⋅f1⋅g1+2⋅f2⋅g0]g_2 = \frac{3}{2}[1 \cdot f_1 \cdot g_1 + 2 \cdot f_2 \cdot g_0] =1.5[0.6×0.08962+0.8×0.04979]= 1.5[0.6 \times 0.08962 + 0.8 \times 0.04979] =1.5[0.05377+0.03983]=1.5×0.09360=0.14041= 1.5[0.05377 + 0.03983] = 1.5 \times 0.09360 = 0.14041. Verification by direct calculation: P(S=2)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)+9e−32(0.36)=0.04979×2.82=0.14041P(N=1)P(X=2) + P(N=2)[P(X=1)]^2 = 3e^{-3}(0.4) + \frac{9e^{-3}}{2}(0.36) = 0.04979 \times 2.82 = 0.14041. Common error: Applying the non-simplified formula incorrectly and getting 0.070200.07020, which is g2/2g_2/2 rather than g2g_2.
Create a Free Account to Access All 152 Questions →

About FreeFellow

FreeFellow is an AI-native exam prep platform for actuarial (SOA & CAS), CFA, CFP, CPA, CAIA, GARP FRM, IRS Enrolled Agent, IMA CMA, and FINRA / NASAA securities licensing candidates — built around modern AI as a core capability rather than as a bolt-on. Every lesson ships with AI-narrated audio. Every constructed-response item has a copy-to-AI prompt builder so candidates can paste their answer into their own ChatGPT or Claude for self-graded feedback. Fellow members get instant AI grading on essays against the official rubric (currently CFA Level III, expanding to other essay-bearing sections).

The 70% you need to pass — question bank, written solutions, lessons, formula sheet, mixed practice, readiness tracking — is free forever, with no trial period and no credit card. Become a Fellow ($59/quarter or $149/year per track) to unlock mock exams, flashcards with spaced repetition, performance analytics, AI essay grading, and a personalized study plan.