ASA exams

ALTAM

Advanced Long-Term Actuarial Mathematics

5 discussions

Study strategy

ALTAM: Show the model, not only the final spreadsheet number

For a long-term calculation, a reviewable answer identifies time, state, probability, discounting and cash flow. A correct total with unexplained formulas is hard to check. Practise organising a small model before relying on a large spreadsheet.

Worked example or practice scenario

Use one row per year with opening lives, survival or decrement assumptions, premium, expense, benefit, discount factor and present value. Run a simple boundary test: no mortality, no lapse and zero interest. The output should reduce to the explicitly scheduled cash flows.

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Then introduce one assumption at a time and explain the direction of change. When preparing for a sitting, use the current official tools and instructions; do not infer spreadsheet permissions from an old forum post.

Reading sources

Official syllabus and resources

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

0 repliesOct 1

Explanation

ALTAM: Multiple-state values require occupancy and transitions

In a health or life model, a benefit may be paid for occupying a state, entering a state or dying from a state. Those payments require different probabilities. A state diagram with labelled cash flows prevents a transition benefit from being treated as an occupancy benefit.

Worked example or practice scenario

In a one-year toy model starting healthy, probabilities at year end are .90 healthy, .08 disabled and .02 dead. A benefit of 500 paid at year end only to disabled lives has expected undiscounted payment 40. A death payment is a separate term.

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Add a benefit payable immediately on entering disability. Explain why the end-of-year disabled probability may omit people who entered disability and recovered within the year. You now need transition timing, not just the final state distribution.

Reading sources

Official syllabus and resources

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

0 repliesOct 1

Explanation

ALTAM: Competing decrements share the same population at risk

Two decrement processes cannot both remove the same person twice. Under specified cause-specific constant forces, total survival uses the sum of forces; each cause’s probability integrates its own force against that survival. Do not add independent single-decrement probabilities.

Worked example or practice scenario

Let annual cause-specific forces be .02 and .03. Total one-year decrement probability is 1−e^−.05≈.04877. Cause 1 receives .02/.05 of that probability, about .01951, under these constant-force assumptions.

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Compare with 1−e^−.02≈.01980 from an isolated single-decrement model. Explain why the competing cause slightly reduces the observed cause-1 probability. Review exactly which assumptions justify converting the rates.

Reading sources

Official syllabus and resources

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

0 repliesOct 1

Explanation

ALTAM: UDD and constant force give different fractional mortality

Annual mortality alone does not determine survival at every fractional age. Uniform distribution of deaths and constant force are additional assumptions. They agree at a full year but can disagree inside it.

Worked example or practice scenario

With annual q=.20, UDD gives half-year survival 1−.5×.20=.90. A constant force consistent with full-year survival .80 gives half-year survival .80^.5≈.89443. The discrepancy is an assumption effect, not rounding error.

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Compute half-year death probability under both assumptions, then conditional survival from time .5 to 1. Under UDD it is .80/.90. State the starting age in each probability so an unconditional and conditional quantity are not confused.

Reading sources

Official syllabus and resources

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

0 repliesOct 1

Explanation

ALTAM: Reserve recursions are cash-flow identities with timing

A one-year recursion connects an opening reserve, premium, interest and conditional benefits to the next reserve. The exact equation depends on premium and claim timing. Define these conventions before memorising a rearrangement.

Worked example or practice scenario

For a discrete toy contract with premium P at the start, death benefit b at the end and next reserve V1 for survivors, (V0+P)(1+i)=q b+p V1. With V0=100, P=20, i=.05, q=.01, b=1,000, p=.99, V1=116/.99≈117.17.

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Check both sides numerically. Then introduce an expense paid at the start and determine which term it reduces. Do not transplant the equation into a continuous-benefit problem without re-deriving the timing.

Reading sources

Official syllabus and resources

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

0 repliesOct 1