ASA exams

FAM

Fundamentals of Actuarial Mathematics

5 discussions

Study strategy

FAM: Keep a two-sided error log for short- and long-term topics

FAM covers both short-term loss models and long-term contingent payments. A single practice score can hide a persistent weakness on one side. Organise mistakes by concept and by cause, not just by question number.

Worked example or practice scenario

A useful log might record “deductible: conditioned on payment instead of loss,” “life benefit: discounted to wrong date,” and “aggregate loss: omitted frequency variance.” Each entry includes the mistaken setup, the corrected variable and one fresh check.

Try this next

Re-solve each example with new numbers after a delay, then mix topics. Use the current official full-FAM syllabus rather than an old FAM-L/FAM-S-only plan. Historical forum study plans are useful themes, but their exam structure may be obsolete.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

FAM: A prospective reserve is a value at a specified time

A reserve compares future benefit and expense cash flows with future premium cash flows on a stated basis. It is not the total premiums already collected. Before calculating, mark which cash flows remain and whether an immediate premium is included.

Worked example or practice scenario

In a deliberately deterministic two-period example, a benefit of 1,100 is due one year from the valuation time and a premium of 300 is due immediately. At 10% interest, the reserve immediately before that premium is 1,100/1.10−300 = 700. Immediately after it, the reserve is 1,000.

Try this next

Add a survival condition and show where its probability enters. State the valuation basis and whether expenses are included. An answer of 700 or 1,000 can be correct only when its timing is clearly defined.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

FAM: Survival and discounting must both match the payment time

A life-contingent benefit requires a financial discount factor and a probability that the relevant condition is met. Survival at the beginning of a period differs from survival at its end. Label the benefit’s timing explicitly.

Worked example or practice scenario

A benefit of 1,000 is payable at time 2 only if a person survives. If annual survival probabilities are .98 then .97, and annual effective interest is 4%, EPV = 1,000×.98×.97/(1.04)² ≈ 878.88.

Try this next

Write the event indicator and discount term before multiplying. Then move the payment to time 1 and recompute. Do not add annual death probabilities when a product of conditional survival probabilities is required.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

FAM: Aggregate loss variance needs both frequency and severity

For independent identically distributed severities independent of frequency, E[S]=E[N]E[X] and Var(S)=E[N]Var(X)+Var(N)E[X]². The second term reflects how many losses occur. Independence assumptions are part of the answer.

Worked example or practice scenario

Let N be Poisson with mean 3, severity mean 100 and variance 4,000. Expected aggregate loss is 300. Variance is 3×4,000 + 3×100² = 42,000. Using only 12,000 treats the loss count as fixed.

Try this next

Replace N with a fixed count of 3 and compare the variance. Next ask what changes if a common weather factor affects both claim frequency and severity; the simple independence formula no longer automatically applies.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1

Explanation

FAM: Payment per loss and payment per payment have different denominators

A deductible creates zero payments on smaller losses. Expected payment per loss includes those zeroes; expected payment conditional on a positive payment does not. Define the payment random variable before calculating its mean.

Worked example or practice scenario

For an exponential loss with mean 1,000 and an ordinary deductible of 200, Y=(X−200)+. E[Y]=1,000 e^−.2 ≈ 818.73. Conditional on X>200, E[Y|Y>0]=1,000 by memorylessness. The two expectations answer different questions.

Try this next

Divide the unconditional mean by P(Y>0)=e^−.2 to verify the conditional mean. Then replace the ordinary deductible with a franchise deductible and write a new payment variable; the formula must change.

Reading sources

Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.

0 repliesOct 1