ACT 330 · Year 3 · Semester 2 · 3 credits · Actuarial

Long-Term Actuarial Mathematics II & Pensions

Master multi-state Markov transitions, universal life profit testing, and defined-benefit pension valuation for Exam ALTAM.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Solvency Horizon

When a century-old mutual insurer discovers a hidden nine-figure deficit across its legacy pension and annuity books, newly appointed supervisory actuary Maya Lin must dismantle and rebuild their valuation models before state regulators force a catastrophic liquidation.

Protagonist · Maya Lin, FSA, a meticulous valuation specialist tasked with auditing Apex Mutual's distressed long-term liability portfolio.

Setting · Apex Mutual's headquarters in Chicago, amid freezing lake-effect storms and late-night regulatory audit rooms.

Stakes · A four-hundred-million-dollar balance sheet shortfall threatens forty thousand retirees with benefit freezes and Apex Mutual with statutory receivership.

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Episodes

Season finale: Maya unveils a dynamically hedged decumulation suite and an unbundled longevity risk transfer that secures regulatory approval, salvages participant solvency, and restores the firm's capital adequacy.

From the lecturer: Welcome to ACT 330. This course covers the advanced mathematics of long-term contingent cash flows, bridging the gap between classical single-decrement life contingencies and modern industry practice as tested on SOA Exam ALTAM. To get the most out of these lecture films: do not watch passively. Keep your financial calculator (BA II Plus or TI-30XS Multiview) and a blank notebook ready. Pause whenever a differential equation, Thiele's ODE, or profit-vector recursion appears on screen. Work through the numerical transitions, Euler discretizations, and pension actuarial cost method reconciliations before I reveal the solution. We move systematically from continuous-time Markov multi-state models through non-diversifiable longevity trends and complex defined-benefit valuations under Projected Unit Credit and Traditional Unit Credit methods. Pay particular attention to the cash-flow projection recursive relations; they form the backbone of both Exam ALTAM and modern asset-liability management modeling in industrial actuarial platforms. Let us begin.

Cold open

At six in the morning, Maya arrives to find Apex's lead long-term disability actuary staring at a terminal showing millions in unexplained statutory reserves. Claims are moving between active, temporary disability, and permanent impairment, but the legacy software uses static mortality tables that treat every disabled life as either permanently lost or instantly dead.

preparing lecture…

Transcript

Formulate continuous-time Markov multi-state insurance and pension models.
Derive Kolmogorov's forward differential equations from the Chapman-Kolmogorov relation.
Calculate state occupancy probabilities and transition probabilities using analytical solutions and numerical stepping.
Evaluate expected present values for continuous state annuities and transition lump-sum benefits.