ACT 301 · Year 3 · Semester 1 · 4 credits · Actuarial

Short-Term Actuarial Mathematics: Loss Models

From individual claim severities to aggregate portfolio tail risk: master the mathematical engine of modern general insurance pricing, reserving, and capital modeling.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Solvency Threshold

When a catastrophic cloud outage triggers cascading commercial liability claims that threaten Meridian Mutual's statutory capital, junior pricing actuary Maya Lin must dismantle and rebuild the company's loss modeling engine from the ground up before the state insurance commissioner shuts down the book.

Protagonist · Maya Lin, an Associate of the Society of Actuaries working as a junior casualty pricing analyst at Meridian Mutual Insurance.

Setting · The actuarial department and executive boardroom of Meridian Mutual in Chicago, alongside regulatory hearings at the Illinois Department of Insurance.

Stakes · A forty-two million dollar reserve deficit that could breach Meridian's Risk-Based Capital minimums, downgrade its AM Best rating to vulnerable, and force the liquidation of its flagship commercial liability portfolio.

Pick an episode

Episodes

Season finale: Maya delivers a fully validated, bootstrap-tested aggregate loss distribution to the state insurance commission and Meridian's board, proving that an optimal combination of layer restructuring, deductible leveraging, and capital allocation restores solvency without forfeiting market share.

From the lecturer: Welcome to ACT 301. This course builds the rigorous probabilistic core for the short-term actuarial exams—specifically SOA Exam FAM (Short-Term component), SOA ASTAM, and CAS MAS-I. Loss modeling is not a spectator sport; you cannot learn it by merely nodding along to derivations. Every lecture requires an open notebook, a standard actuarial calculator (such as the TI-30XS MultiView), and an active Python environment for empirical validation. As we move from continuous severity distributions and discrete (a,b,0)/(a,b,1) frequency classes to coverage modifications, Panjer recursion, and likelihood construction under truncation and censoring, write down every likelihood and recurrence relation by hand before computing. When an aggregate distribution is derived analytically, verify your solution against a Monte Carlo simulation. Pay meticulous attention to the subtle distinction between per-loss and per-payment random variables, as well as ground-up versus modified loss perspectives. Master these foundations here, and you will command the exact statistical mechanics used by actuaries worldwide to price catastrophic excess-of-loss treaties and quantify extreme underwriting risk.

Cold open

At 7:42 AM on a rainy Tuesday, Maya Lin arrives at her desk to find three voicemail messages from Chief Actuary Elena Vance. Meridian's mid-market cyber liability portfolio has just logged five unexpected seven-figure claims in forty-eight hours, and the legacy exponential severity model predicts a probability of less than one in ten million for this cluster.

preparing lecture…

Transcript

Define and interpret survival functions, hazard rates, and mean excess loss functions
Classify continuous severity distributions by tail heaviness using asymptotic hazard rates and survival ratios
Calculate tail probabilities and raw moments for benchmark loss distributions (Exponential, Pareto, Gamma, Lognormal, Weibull)
Evaluate the actuarial implications of heavy tails in commercial pricing and capital modeling for SOA FAM and CAS MAS-I