ASTAM Formula Sheet and Notation
The ASTAM formula and notation layer is not a substitute for modeling fluency. It tells you the exam's symbols and supplied references; you still need to recognize the model, define the random variables, and explain the actuarial meaning of each calculation.
Quick Answer
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.
Notation To Know Cold
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.
Policy Modification Vocabulary
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.
Risk Measure Conventions
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.
What Still Needs Memory
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.
Original Source-Backed Practice
4 questions built from syllabus outcomes and released-exam patterns. The prompts and answers are original, so they train the skill without copying official exam text.
ASTAM Formula and Notation Flashcards
Short ASTAM checks for notation, payment variables, tail-risk conventions, and reserving vocabulary.
- Question 1/Flashcard
Deductible with a payment limit
A ground-up loss X has ordinary deductible d and an insurer payment limit u. Write the insurer payment random variable Y.
Solution And Grading Points
Y = min(max(X - d, 0), u). The limit u is on the insurer payment, not on the ground-up loss, unless the contract says otherwise.
- Uses max(X - d, 0) for the ordinary deductible.
- Caps the insurer payment at u.
- Separates payment limit language from maximum covered loss language.
- Question 2/Flashcard
Outstanding claims versus IBNR
Explain the difference between an outstanding claims reserve and IBNR in one or two sentences.
Solution And Grading Points
The outstanding claims reserve covers incurred but unsettled claims. IBNR is the portion for claims that have been incurred but not yet reported, so it is only part of the unpaid-claim picture.
- States that outstanding claims are incurred but unsettled.
- States that IBNR means incurred but not reported.
- Avoids treating all unpaid claims as IBNR.
- Question 3/Flashcard
Expected Shortfall convention
What does ES_alpha average when the loss quantile function is Q_u?
Solution And Grading Points
ES_alpha averages the upper-tail quantiles above alpha: ES_alpha = (1 / (1 - alpha)) times the integral of Q_u from alpha to 1.
- Identifies the average as an upper-tail quantile average.
- Uses the range from alpha to 1.
- Keeps the loss convention rather than switching to gain notation.
- Question 4/Flashcard
Excess-of-loss translation
Why can excess-of-loss reinsurance be treated like a deductible from the reinsurer's perspective?
Solution And Grading Points
The reinsurer pays only the part of the loss above an attachment point, possibly capped by a limit. That payment shape matches a deductible-and-limit payment variable.
- Names the attachment point.
- Connects reinsurer payment to the excess over the attachment.
- Mentions the possible cap when a layer limit exists.