Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Lessons

All 36 SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) lessons are free to read, each with worked examples and audio narration. No signup required.

Survival Models for Contingent Cash Flows

• Understand and explain features of typical mortality curves and heterogeneities in mortality. (10 min)
• Apply Markov multiple state models to state-contingent life and long-term health insurance benefits, and Continuing Care Retirement Communities (CCRCs). (29 min)
• Understand and critique the assumptions underlying Markov multiple state models for long-term insurance benefits. (8 min)
• Derive and apply Kolmogorov's forward equations for continuous time Markov multiple state models. (40 min)
• Calculate state-dependent probabilities for continuous time Markov models. (19 min)
• Apply the Chapman-Kolmogorov equations to calculate discrete time transition probabilities in the Markov model. (9 min)
• Construct and deconstruct multiple decrement tables using the associated single decrement models and appropriate fractional age assumptions. (27 min)
• Calculate maximum likelihood estimates of transition intensities and probabilities for multiple state and multiple decrement models, assuming piecewise constant transition intensities. (10 min)
• Calculate approximate confidence intervals for the estimators in Topic 1(h), using asymptotic properties of the maximum likelihood estimators. (7 min)

Premium and Policy Valuation for Long-Term Coverages

• Define and interpret state-dependent insurance and annuity present value random variables and identify and calculate their expected values. (37 min)
• Derive and apply two-term and three-term Woolhouse approximations for calculating expected present values of state-dependent cash flows. (13 min)
• Calculate premiums for state-dependent life insurance, long-term health insurance, and CCRCs using the equivalence principle. (63 min)
• Calculate policy values for state-dependent life insurance, long-term health insurance, and CCRCs. (87 min)
• Identify and apply Thiele's differential equation in a single life or multiple state setting. (12 min)

Joint Life Insurance and Annuities

• Understand how joint-life mortality can be modelled using (i) a time-to-status-failure random variable, and (ii) a multiple state model. (42 min)
• Understand the implications of independence or dependence of future lifetimes in both versions of the joint life model. Identify sources of dependence and understand how they are accommodated in the models. (43 min)
• Calculate premiums for insurance and annuities on joint lives using the equivalence principle. (80 min)
• Calculate policy values for insurance and annuities on joint lives. (62 min)

Profit Analysis

• Calculate and interpret expected profit and actual profit. (38 min)
• Analyze and interpret gains by source. (40 min)
• Calculate 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. (77 min)
• Calculate premiums for long-term life and health insurance and annuity contracts based on a specified profit objective. (11 min)
• Calculate reserves for long-term life and health insurance and annuity contracts using profit testing. (11 min)

Pension Plans and Retirement Benefits

• Calculate 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. (36 min)
• Calculate the required contribution rate to meet a target replacement ratio for a DC plan participant, using a deterministic approach. (49 min)
• Identify, interpret, and apply service table and salary scale functions for pension plan valuation. (11 min)
• For a DB plan, calculate and interpret accrued benefits, including benefits on early exit from the plan. (30 min)
• For 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. (41 min)

Universal Life Insurance

• Understand the cashflows and calculate account values and benefits under Type A and Type B Universal Life policies. (48 min)
• Calculate reserves for no-lapse guarantees. (15 min)
• Use 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 assumptions. (36 min)

Embedded Options in Life Insurance and Annuity Products

• Define 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, and guaranteed minimum withdrawal benefit. (10 min)
• Value the following options embedded in insurance and annuity contracts, using the Black-Scholes model: guaranteed minimum death benefit, and guaranteed minimum accumulation/maturity benefit. (33 min)
• Construct a replicating portfolio for the options in 7(b) using delta-hedging. (12 min)
• Understand and evaluate the costs associated with discrete-time rebalancing. (12 min)
• Use 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. (44 min)