ACT 310 · Year 3 · Semester 1 · 3 credits · Actuarial

Ratemaking & Credibility

From historical loss triangles to tomorrow's rate filing: the mathematical engine of P&C pricing and credibility theory.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

The Rate Filing

When a regional commercial insurer faces sudden insolvency from runaway liability claims, lead pricing actuary Maya Lin must rebuild the entire ratemaking engine from raw exposure counts to empirical Bayes credibility before the state insurance commissioner shuts them down.

Protagonist · Maya Lin, ACAS, newly appointed Lead Ratemaking Actuary at Apex Mutual Insurance.

Setting · Apex Mutual headquarters in Chicago and the hearing chambers of the Illinois Department of Insurance.

Stakes · A forty-two million dollar reserve deficit and imminent regulatory takeover if Maya cannot present a rigorously justified, mathematically airtight rate filing across all commercial lines.

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Episodes

Season finale: Maya defends the multi-tiered Bühlmann-Straub credibility model before the Insurance Commissioner, proving that empirical Bayes parameter estimation prevents adverse selection while stabilizing rates for small businesses.

From the lecturer: Welcome to ACT 310. This course forms the mathematical and practical bedrock for CAS Exam 5 (Basic Techniques for Ratemaking and Estimating Claim Liabilities) and the credibility foundations tested on SOA Exam ASTAM. In P&C actuarial practice, raw accounting data is never ready for pricing: you must adjust historical premiums for rate level history, develop claims to their ultimate value, project frequency and severity trends through macroeconomic shifts, and isolate fixed from variable expenses. When you divide a portfolio into pricing risk cells, data becomes thin, requiring credibility theory to strike an optimal bias-variance balance. Keep a pad of graph paper ready for every lecture to draw rate change parallelograms and loss development triangles by hand before inspecting the code. Calculate every intermediate step alongside the derivations: understanding how classical limited-fluctuation credibility transitions into Bayesian Bühlmann-Straub shrinkage is essential for both your actuarial credentials and modern machine learning feature engineering. Master the dual paths of the pure premium and loss ratio methods until the algebra is second nature.

Cold open

At six in the morning on a rainy Tuesday, Maya Lin opens the commercial auto portfolio ledger and finds an alarming discrepancy: earned premium grew by twelve percent while written car-years collapsed by twenty percent. The executive team thinks revenue is booming, but Maya realizes they are charging yesterday's rates on a shrinking, riskier fleet.

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Transcript

Evaluate candidate exposure bases against the four fundamental ratemaking criteria
Calculate written, earned, unearned, and in-force exposures under uniform and exact policy distribution models
Distinguish calendar year, policy year, and accident year exposure and premium aggregations
Formulate exposure as an offset in generalized linear models for loss frequency