What This Exam Validates
The Advanced Long-Term Actuarial Mathematics Exam assesses professional knowledge regarding contingent payment models and financial risk applications. Certified and administered by the Society of Actuaries, this extensive testing instrument evaluates technical analytical skills across seven distinct core content domains required for professional actuarial practice in long-term financial markets.
Who Should Take This Exam
Actuarial candidates actively pursuing professional credentials who have successfully completed prior mandatory requirements such as prerequisite examinations and seek complete mastery in long-term models and financial risk applications.
Skills You Should Be Ready to Demonstrate
- Survival Models
- Policy Valuation
- Joint Life
- Profit Analysis
- Pension Plans
- Universal Life
- Embedded Options
How to Prepare
Review the official syllabus, curriculum documents, and detailed study materials provided directly by the Society of Actuaries. Practice extensively with prior examination questions and official model solutions to fully understand question formats, calculation methodologies, and appropriate written responses for the $500 test format.
Domain Study Guidance
Survival Models for Contingent Cash Flows: Study Guidance
This specific domain thoroughly covers survival models for contingent cash flows, carefully analyzing typical mortality curves, addressing individual heterogeneities in mortality, and applying Markov multiple state models to long-term health insurance benefits.
- Explain mortality curves and heterogeneities
- Apply Markov multiple state models to long-term health insurance
Premium and Policy Valuation for Long-Term State-Dependent Coverages: Study Guidance
This domain focuses on premium calculations and policy valuation for state-dependent coverages, requiring candidates to derive approximations and compute expected present values using established actuarial principles and formulas.
- Define present value random variables
- Derive Woolhouse approximations
- Calculate premiums using the equivalence principle
Joint Life Insurance and Annuities: Study Guidance
This domain examines joint life insurance and annuity products using time-to-status-failure random variables alongside multiple state models, analyzing both independence and dependence of future lifetimes in actuarial practice.
- Model joint-life mortality
- Analyze independence and dependence of future lifetimes
Profit Analysis: Study Guidance
This specific analytical domain extensively explores profit analysis, expected versus actual profit comparisons, gains by source calculations, and crucial financial metrics like profit signatures, internal rates of return, and profit margins.
- Calculate profit signatures and vectors
- Analyze internal rate of return and profit margin
Pension Plans and Retirement Benefits: Study Guidance
This domain addresses pension plans, retirement benefits, and replacement ratios, requiring candidates to apply service table and salary scale functions for accurate pension plan valuation within defined benefit frameworks.
- Calculate replacement ratios for Defined Benefit and Defined Contribution plans
- Apply service table and salary scale functions
Universal Life Insurance: Study Guidance
This domain evaluates universal life insurance account values, cash flows, reserves for no-lapse guarantees, and emerging surplus utilizing deterministic profit testing under various estimation and stress test assumptions.
- Calculate account values for Type A and Type B policies
- Assess reserves for no-lapse guarantees
Embedded Options in Life Insurance and Annuity Products: Study Guidance
This domain analyzes embedded options in life insurance and annuity products, defining specific guaranteed minimum benefits and valuing those options using the Black-Scholes model and delta-hedging replicating portfolios.
- Define payoffs under guaranteed minimum benefits
- Value options using the Black-Scholes model
Exam-Day Guidance
The 180-minute examination includes six questions worth 60 points total, delivered professionally through Prometric. Check directly with the Society of Actuaries for official registration details and testing rules.
Frequently asked questions
How many questions are on the exam?
The examination consists of precisely six questions worth a total of 60 points, which includes one Excel workbook question and five separate booklet questions for candidates.
What is the passing score?
The official passing score requirement for this specific examination is unfortunately not published publicly on the retrieved Society of Actuaries pages for candidates to review.
How long is the exam?
The formal examination is administered as a structured 180-minute testing appointment conducted at an authorized Prometric testing center location for all registered examinees taking this assessment.
What is the fee for the exam?
The official registration fee required to take the examination is exactly $500 as clearly listed on the official Society of Actuaries website and study guides.
Sources and Verification
Verified 2026-09-13
How this page was made
This detailed overview and structural summary is built directly from official Society of Actuaries documentation, syllabi, and published study materials available online.
Exam Domains
1.0 Survival Models for Contingent Cash Flows
15%
- 1.1Understand and explain features of typical mortality curves and heterogeneities in mortality.
- 1.2Apply Markov multiple state models to state-contingent life and long-term health insurance benefits, and Continuing Care Retirement Communities (CCRCs).
- 1.3Understand and critique the assumptions underlying Markov multiple state models for long-term insurance benefits.
- 1.4Derive and apply Kolmogorov’s forward equations for continuous time Markov multiple state models.
- 1.5Calculate state-dependent probabilities for continuous time Markov models.
- 1.6Apply the Chapman-Kolmogorov equations to calculate discrete time transition probabilities in the Markov model.
- 1.7Construct and deconstruct multiple decrement tables using the associated single decrement models and appropriate fractional age assumptions.
- 1.8Calculate maximum likelihood estimates of transition intensities and probabilities for multiple state and multiple decrement models, assuming piecewise constant transition intensities.
- 1.9Calculate approximate confidence intervals for the estimators in Topic 1(h), using asymptotic properties of the maximum likelihood estimators.
2.0 Premium and Policy Valuation for Long-Term State-Dependent Coverages
16%
- 2.1Define and interpret state-dependent insurance and annuity present value random variables and identify and calculate their expected values.
- 2.2Derive and apply two-term and three-term Woolhouse approximations for calculating expected present values of state-dependent cash flows.
- 2.3Calculate premiums for state-dependent life insurance, long-term health insurance, and CCRCs using the equivalence principle.
- 2.4Calculate policy values for state-dependent life insurance, long-term health insurance, and CCRCs.
- 2.5Identify and apply Thiele’s differential equation in a single life or multiple state setting.
3.0 Joint Life Insurance and Annuities
12%
- 3.1Understand how joint-life mortality can be modelled using (i) a time-to-status-failure random variable, and (ii) a multiple state model.
- 3.2Understand the implications of independence or dependence of future lifetimes in both versions of the joint life model from 3(a). Identify sources of dependence and understand how they are accommodated in the models.
- 3.3Calculate premiums for insurance and annuities on joint lives using the equivalence principle.
- 3.4Calculate policy values for insurance and annuities on joint lives.
4.0 Profit Analysis
15%
- 4.1Calculate and interpret expected profit and actual profit.
- 4.2Analyze and interpret gains by source.
- 4.3Calculate and interpret profit signature, profit vector, net present value, internal rate of return, profit margin, and discounted payback period for long-term life and health insurance, and annuity contracts.
- 4.4Calculate premiums for long-term life and health insurance and annuity contracts based on a specified profit objective.
- 4.5Calculate reserves for long-term life and health insurance and annuity contracts using profit testing.
5.0 Pension Plans and Retirement Benefits
14%
- 5.1Calculate replacement ratios for Defined Contribution (DC), and Defined Benefit (DB) plans, including final average salary (FAS), career average earnings (CAE), and career average revalued earnings (CARE) plans.
- 5.2Calculate the required contribution rate to meet a target replacement ratio for a DC plan participant, using a deterministic approach.
- 5.3Identify, interpret, and apply service table and salary scale functions for pension plan valuation.
- 5.4For a DB plan, calculate and interpret accrued benefits, including benefits on early exit from the plan.
- 5.5For a DB plan, calculate and interpret the actuarial accrued liability and the normal cost for benefits payable on age retirement or early exit using the projected unit credit (PUC) and traditional unit credit (TUC) valuation methods.
6.0 Universal Life Insurance
14%
- 6.1Understand the cashflows and calculate account values and benefits under Type A and Type B Universal Life policies.
- 6.2Calculate reserves for no-lapse guarantees.
- 6.3Use deterministic profit testing to calculate premiums or reserves, and assess emerging surplus for Universal Life insurance, including profit signature, profit vector, net present value, internal rate of return, profit margin, and discounted payback periods, under best estimate or stress test assum
7.0 Embedded Options in Life Insurance and Annuity Products
14%
- 7.1Define and calculate payoffs under each of the following options embedded in insurance and annuity contracts: Guaranteed minimum death benefit; Guaranteed minimum maturity benefit; Guaranteed minimum income benefit; Guaranteed minimum withdrawal benefit.
- 7.2Value the following options embedded in insurance and annuity contracts, using the Black-Scholes model: Guaranteed minimum death benefit; Guaranteed minimum accumulation/maturity benefit.
- 7.3Construct a replicating portfolio for the options in 7(b) using delta-hedging.
- 7.4Understand and evaluate the costs associated with discrete-time rebalancing.
- 7.5Use deterministic profit testing to assess emerging surplus for equity-linked life insurance cash flows, including profit signature, profit vector, net present value, internal rate of return, profit margin, and discounted payback periods, under best estimate or stress test assumptions.