ASTAM Formula Sheet and Notation

The Spring 2026 ASTAM syllabus lists a formula sheet and a notation and terminology note among the official resources. The notation note standardizes accident-year, calendar-year, development-year, policy-modification, risk-measure, and reserving language.

Study the formula layer as a translation aid, not as the study plan itself. Most lost points come from choosing the wrong model, using the wrong coverage definition, or failing to explain the result, not from being unable to copy a formula.

Claim-frequency and severity notation is basic but easy to misuse under pressure: p(k) or p_k for a discrete probability function, f(x) for a continuous density, F(x) for a distribution function, and S(x) for survival. Frequency and severity are assumed independent unless the problem says otherwise.

For reserving, keep AY, CY, and DY separate. ASTAM uses outstanding claims reserve for incurred but unsettled claims. IBNR refers only to incurred but not reported claims inside that larger reserve, not every unpaid claim.

The notation note makes a few exam-specific word choices explicit. Coinsurance is from the insurer's perspective: c percent coinsurance means the insurer pays c percent. A policy limit is the maximum insurer payment, while maximum covered loss is the loss level above which no extra benefit is paid.

Excess-of-loss reinsurance looks like a deductible from the reinsurer's perspective. Quota share looks like coinsurance. These analogies are high-yield because coverage-modification questions often test whether you can translate the contract wording before calculating.

ASTAM uses the alpha Value-at-Risk as the alpha quantile of the loss distribution. Expected Shortfall is the average quantile in the upper tail above alpha. The note also flags that ES, CTE, and Tail VaR are often used for the same practical idea in contemporary actuarial work.

For exam answers, state the quantile convention before calculating. That one sentence prevents a lot of tail-probability ambiguity.

Memorize the recognition rules, not just the formulas: which frequency families belong to the Panjer classes, how deductibles and limits change the payment variable, what Mack's assumptions say, when Buhlmann-Straub exposure weights matter, and how AIC or BIC turns a likelihood into a model-selection decision.

Your formula-sheet routine should be short: identify the topic, write the random variable, define the contract modification or triangle cell, then pull the formula. Pulling formulas first is the slow path.