Prepare for ALTAM against the October 2026 syllabus: seven topics, each weighted roughly 8-20%, tested in a three-hour, six-question, 60-point format at Prometric with one Excel-based question. Build one reusable setup habit per concept: define states and transitions before computing, derive reserves from recursions, keep profit vectors and signatures distinct, fix a deduction order in universal life roll-forwards, and reconcile results against a second method. Work past ALTAM exams untimed first, then timed.
What the ALTAM exam covers
ALTAM is the SOA's advanced exam on long-term contingent mathematics: survival models, state-dependent insurance and annuity valuation, joint lives, profit testing, pensions, universal life, and embedded options. Knowledge of the FM, P, and FAM exams and the Mathematical Statistics VEE material is assumed.
The Advanced Long-Term Actuarial Mathematics (ALTAM) Exam sits in the SOA's associate-level pathway after the Fundamentals of Actuarial Mathematics (FAM) exam. The SOA's study page names FAM as the assumed prior component, and the October 2026 syllabus adds that FM, P, and the Mathematical Statistics VEE material are also assumed.
Coverage spans seven topics, from multiple state survival models through profit analysis, pension funding, universal life, and equity-linked guarantees. The syllabus is the governing document: start there, and check its Updates page periodically for corrections. Everything in this guide reflects the October 2026 edition.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF; Studying for Advanced Long-Term Actuarial Mathematics (ALTAM) Exam — SOA ALTAM study page
Exam format: one Excel question, five handwritten answers
ALTAM is a three-hour exam with six questions worth 60 points, taken at a Prometric test center. Five questions are answered in pen in an answer booklet; one question is completed in an Excel workbook that the SOA grades from your uploaded file.
The format matters for preparation. The Excel Workbook provided at the exam contains the Excel question plus tables and formulas you may use for any of the six questions. For the five handwritten questions, you may use Excel for calculations, but only what you write in the answer booklet is graded. For the Excel question, only the workbook is graded.
Scratch paper is available for rough notes, but nothing written there earns credit. The Formula Sheet and the Exam ALTAM Tables are available on the computer, while the textbook and study notes are not provided at the exam. At the end, you upload the workbook and hand in the answer booklets.
Practicing at least a few full questions inside Excel, including formatting a graded answer clearly in a cell, is therefore not optional polish. It rehearses the actual scoring channel for one sixth of the exam.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
The seven topics and their weights
Every topic carries a weight between 8% and 20%, so no single area dominates. Long-term care and CCRC material is tested inside the survival model and valuation topics rather than as a standalone heading.
The table below maps the official topic list from the October 2026 syllabus. Note that CCRCs (continuing care retirement communities) and long-term health insurance appear within Topics 1 and 2 as applications of state-contingent models, which answers a common question about where that material lives.
The weights confirm the guide's structure: multiple state machinery underpins the two heaviest topics, and profit testing reappears again inside the universal life and embedded options outcomes.
| Topic | Weight |
|---|---|
| 1. Survival Models for Contingent Cash Flows | 10-20% |
| 2. Premium and Policy Valuation for Long-Term State-Dependent Coverages | 12-20% |
| 3. Joint Life Insurance and Annuities | 8-16% |
| 4. Profit Analysis | 10-20% |
| 5. Pension Plans and Retirement Benefits | 10-18% |
| 6. Universal Life Insurance | 10-18% |
| 7. Embedded Options in Life Insurance and Annuity Products | 10-18% |
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Setting up a multiple state model before computing
Decide the states, the allowed transitions, and whether the intensities are constant or time-dependent before touching any formula. Most long calculations unravel because the setup never matched the question's stated assumptions.
A multiple state model is fully specified by its states, its permitted transitions, and the transition intensities between them. Write the intensity structure first, mark disallowed transitions as zero, and convert verbal conditions such as a recovery option available only in the first year into explicit time-dependence. The syllabus outcomes include deriving Kolmogorov's forward equations, computing state-dependent probabilities, and applying the Chapman-Kolmogorov equations for discrete-time transitions, so this setup step feeds nearly every Topic 1 question.
Distinguish independent rates from dependent ones. In a multiple decrement setting, decrements compete, so a table of independent probabilities must be converted through associated single decrement models before it describes the competing-risks model; intensities given directly can be used as they stand. Topic 1 also expects maximum likelihood estimation of transition intensities under piecewise-constant assumptions, with approximate confidence intervals from asymptotic theory.
Worked examples and the solved exercise on this page are original practice problems, not past exam questions.
Assume an active/sick/dead model with constant transition intensities over the year: active to dead 0.02, active to sick 0.05, sick to dead 0.08, and sick to active 0.10. Death is absorbing. Using the standard constant-intensity formulas, compute the one-year transition probabilities and verify each row sums to 1.
Each worked example includes its complete solution and reasoning below the prompt.
Active row: active to active = e^(-0.07) = 0.9324; active to sick = (0.05/0.07)(1 - e^(-0.07)) = 0.7143 x 0.06761 = 0.0483; active to dead = (0.02/0.07)(1 - e^(-0.07)) = 0.2857 x 0.06761 = 0.0193. Row sum: 0.9324 + 0.0483 + 0.0193 = 1.0000. Sick row: sick to sick = e^(-0.18) = 0.8353; sick to active = (0.10/0.18)(1 - e^(-0.18)) = 0.5556 x 0.16473 = 0.0915; sick to dead = (0.08/0.18)(1 - e^(-0.18)) = 0.4444 x 0.16473 = 0.0732. Row sum: 0.8353 + 0.0915 + 0.0732 = 1.0000. Dead row: 1.
Under constant total exit intensity, the probability of staying put is the exponential of minus the total exit force, and each exit probability splits the non-exit mass (1 minus that exponential) in proportion to its share of the total force. The row sums of 1 are the built-in check the exercise asks for. The explicit recovery transition matters: collapsing the model to two states would force all sick lives to stay sick for the whole year, which understates transitions back to the active state and every valuation that depends on them.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Reserves and Thiele's differential equation
A state's reserve is the expected present value of future benefits minus future premiums from that state. It satisfies both a continuous differential equation (Thiele's equation, named in the syllabus outcomes) and a discrete year-by-year recursion; if the two disagree, cash-flow timing or the basis is inconsistent.
The syllabus asks you to identify and apply Thiele's differential equation in single-life and multiple state settings. Build the habit of checking one representation against the other: with simple assumptions, solving the continuous form and stepping the recursion should land on the same values at integer durations. Divergence points to premium or benefit timing, not arithmetic.
A small case shows why timing must be fixed in writing. Assume a whole-life death benefit of 1000, constant mortality force 0.04, and interest force 0.05. If the benefit is paid at the moment of death, the continuous reserve is 1000 x 0.04/(0.04 + 0.05) = 444.44. If the same benefit is instead paid at the end of the year of death, the discrete whole-life EPV works out to about 439, using q = 1 - e^(-0.04) = 0.0392 and v = 1/1.05. The gap between 444 and 439 is not an error; it is the discounting of the payment date. Label every cash flow's timing and basis before you compute, and no downstream result inherits a silent assumption.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Profit vectors versus profit signatures
The profit vector holds emerging profit per policy in force at each duration; the signature multiplies each entry by the cumulative survival probability to the start of that year. Pricing measures such as the net profit margin belong to the signature, not the vector.
The syllabus lists expected and actual profit, gains by source, and the signature, vector, NPV, IRR, profit margin, and discounted payback period as Topic 4 outcomes. Reserves are computed on a reserve basis while the projected cash flows use the profit basis; every difference between those bases generates profit as an interest, mortality, or expense margin. Annotate each term of your recursion with its basis so that an odd result traces to a specific margin.
Worked example. Assume a three-year term policy with premium 100 at each start of year, sum insured 5000, q = 0.01 each year, an issue expense of 5, profit-basis interest 5%, and reserves of 0, 100, and 205 at the starts of years 1 to 3. The yearly profit is: year 1: (0 + 100 - 5)(1.05) - 0.01 x 5000 - 0.99 x 100 = -49.25; year 2: (100 + 100)(1.05) - 50 - 0.99 x 205 = -42.95; year 3: (205 + 100)(1.05) - 50 = 270.25. Read these carefully: the year-3 figure belongs only to policies still in force. Weighting by cumulative survival to the start of each year (1, 0.99, 0.99^2) gives a signature of -49.25, -42.52, and 264.87. Because pricing adequacy is judged per policy issued, the unweighted vector overstates later-year profit.
| Measure | What it holds | Built from | Use it for |
|---|---|---|---|
| Profit vector | Emerging profit per policy in force at each duration | Recursive cash-flow projection with reserve and profit bases | Seeing when profit emerges and which margin drives it |
| Profit signature | Profit per policy issued, weighted by cumulative survival | Profit vector entries multiplied by cumulative survival to date | Net profit margin, return measures, pricing comparisons |
| Present value of signature | Discounted per-issue profit across the term | Signature entries discounted at a risk discount rate | Judging overall contract adequacy in one figure |
| Reserve held | Funds required at a duration under the reserve basis | Expected value of future benefits minus future premiums | Balance-sheet quantities feeding the profit test recursion |
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Universal life account values and deduction order
An account value update follows a declared sequence of premium, expense charges, cost of insurance, and credited interest. Fix the order, recompute the net amount at risk every period, and keep pricing cost-of-insurance rates separate from expected mortality.
Name the components first: account value, face amount, net amount at risk (face minus account value), cost of insurance, expense charges, and credited interest. The syllabus covers Type A and Type B designs, no-lapse guarantee reserves, and deterministic profit testing under best-estimate or stressed assumptions. The deduction order changes the answer because the cost of insurance depends on the account value remaining when it is calculated.
Illustrative roll-forward: account value 10,000, premium 1,200, expense charge 60, so the value after premium and expense is 11,140. Cost of insurance at 0.002 on a face of 100,000 is 0.002 x (100,000 - 11,140) = 177.72; credited interest is 4%. Deducting cost of insurance before interest gives (11,140 - 177.72) x 1.04 = 11,400.77; deducting it after interest gives 11,140 x 1.04 - 177.72 = 11,407.88. The gap compounds in a monthly model and redistributes profit across periods.
In profit tests, the identifiable margins are the cost-of-insurance spread (pricing rate versus expected mortality) and the interest spread between credited and earned rates. If the sequencing shifts between attempts, you can mistake a mechanical timing effect for a genuine margin change, so the order belongs on your setup sheet beside the bases.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Preparing for pensions, joint lives, and embedded options
Topics 3, 5, and 7 have their own calculation toolkits. Treat them as preparation priorities straight from the official outcomes, and use the prescribed textbook chapters and sample materials rather than generic retirement or derivatives notes.
For pensions, the outcomes focus on replacement ratios for defined contribution and defined benefit designs (including final average salary, career average earnings, and career average revalued earnings), contribution rates for a DC target, service tables and salary scales, accrued benefits on early exit, and the projected unit credit and traditional unit credit methods for actuarial accrued liability and normal cost. Working each of these calculation types once by hand, from the definitions in the prescribed text, is a sound preparation step.
For joint lives, practice both modeling routes the syllabus names: a time-to-failure random variable and a multiple state model, including how independent or dependent future lifetimes change premiums and policy values. For embedded options, the outcomes cover the four guarantee types (death, maturity, income, and withdrawal benefits), Black-Scholes valuation of death and maturity guarantees, delta-hedging replicating portfolios, the cost of discrete rebalancing, and deterministic profit tests on equity-linked cash flows.
Do not neglect the estimation and approximation outcomes in Topic 2: two-term and three-term Woolhouse approximations for expected present values appear explicitly in the syllabus. The equivalence-principle premium and policy value calculations for state-dependent coverages, including CCRC and long-term health designs, are the connective tissue across Topics 1, 2, and 3.
- Core text: Dickson, Hardy and Waters, Actuarial Mathematics for Life Contingent Risks, third edition, with the specific chapter and section list in the syllabus (exercises count as required reading).
- Supplementary reading: ALTAM-21-23 on variable annuity guarantees.
- Official aids: the ALTAM notation and terminology note, exam tables, Excel workbook, formula sheet, sample questions, and sample Excel questions.
- Past exams: past LTAM exams from October 2018 through 2022 and past ALTAM exams from Spring 2023 onward are on the SOA website; because syllabi evolve, not every prior question matches the current exam.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF
Fees, registration, and next steps
The 2026 fee for ALTAM is $500 USD, with electronic access to required study notes included. Register online or by application through the SOA, and confirm current deadlines on the official registration pages.
The SOA's fee page lists ALTAM at $500 for 2026 and notes that all fees are subject to change. Reduced exam fees, reimbursement, and scholarships are available to eligible candidates, and outstanding fees must be paid before enrolling in future exams.
A practical sequence, offered as advice rather than an official requirement: read the October 2026 syllabus and the Introductory Study Note, work through the textbook chapters and sample questions topic by topic, then move to past ALTAM exams untimed to practice setup, and finally timed. Check the Updates page on the exam home page periodically, since corrections are posted there.
- Confirm registration windows and exam-day rules on the SOA's official ALTAM pages before booking.
- Practice at least one full question end to end in the Excel workbook format.
- Download the formula sheet and exam tables in advance so their layout is familiar on exam day.
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.: Exam and e-Learning Module Fees — Updated December 16, 2025; 2026 ASA exam fees; SOA Advanced Long-Term Actuarial Mathematics October 2026 syllabus, format, learning outcomes, weights, and readings — October 2026 ALTAM syllabus PDF; Studying for Advanced Long-Term Actuarial Mathematics (ALTAM) Exam — SOA ALTAM study page
Facts checked against the SOA October 2026 ALTAM syllabus, the SOA study page, the past exams page, and the SOA fee page retrieved in September 2026.
Exam length, question count, point total, assumed knowledge, topic weights, format, and the 2026 fee verified against SOA sources.: