SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) Glossary
28 essential terms and definitions for SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics). Each definition is written for exam preparation, covering the concepts as they are tested on the 2026 syllabus.
A
- Aggregate Excess Reinsurance
- Aggregate excess reinsurance responds when the cedant's aggregate losses for a period exceed a retention. It protects against accident-year volatility rather than against individual large losses.
- Allocated Loss Adjustment Expense (ALAE)
- ALAE is the claim-handling expense that can be tied to a specific claim, such as defense costs in a liability claim. It is typically included with losses for ratemaking and reserving purposes.
B
- Bornhuetter-Ferguson Method
- The Bornhuetter-Ferguson method is a loss-reserving technique that blends chain-ladder development factors with an a-priori expected loss ratio. It reduces volatility for less mature accident years where chain-ladder is unstable.
- Bornhuetter-Ferguson Reserve
- The BF reserve estimate equals the a-priori expected losses multiplied by the unreported percentage. It is structurally a hybrid that gives weight to both the prior expectation and the observed development pattern.
C
- Catastrophe Reinsurance
- Catastrophe reinsurance protects the cedant against losses from large-scale events such as hurricanes, earthquakes, or pandemics. It typically attaches at a very high retention with annual aggregate limits and is priced using catastrophe models.
- Cession (Reinsurance)
- A cession is the portion of a risk the primary insurer (cedant) transfers to a reinsurer. The reinsurer's accepted portion is its assumption; cession and assumption are mirror sides of the same transaction.
- Combined Ratio
- The combined ratio is the sum of the loss ratio and the expense ratio. A combined ratio below 100% indicates underwriting profit (before investment income); above 100% indicates underwriting loss.
- Conditional Tail Expectation (CTE)
- Conditional tail expectation at confidence α is the expected loss given that loss exceeds VaR at that confidence level. It is a coherent risk measure (sub-additive) and is tail-sensitive in ways VaR is not.
- Credibility (Buhlmann)
- Buhlmann credibility minimizes squared error in blending experience with the prior. The credibility factor Z increases with the number of exposures and decreases with the variance of hypothetical means relative to expected process variance.
E
- Earned premium is the portion of written premium attributable to coverage already provided. It is recognized pro-rata over the policy period and is the appropriate denominator for the loss ratio.
- Excess of Loss Reinsurance (XL)
- Excess of loss reinsurance covers each loss above a per-loss retention up to a limit. Structures include per-risk XL (each risk), per-occurrence XL (each event), and clash XL (multiple insureds in one event).
- Exposure-Based Ratemaking
- Exposure-based ratemaking builds the rate from expected loss per exposure unit (pure premium) plus loadings. It is preferred when historical experience is limited or when changes in exposure mix make historical data unrepresentative.
F
- Frequency-Severity Ratemaking
- Frequency-severity ratemaking estimates expected claim frequency (claims per exposure) and expected severity (loss per claim) separately. Their product is the pure premium; loadings produce the gross rate.
I
- Incurred but Not Reported (IBNR)
- IBNR losses are claims that have occurred but have not yet been reported to the insurer. It is a key component of loss reserves and the focus of much of reserving methodology.
L
- Loss Adjustment Expense (LAE)
- Loss adjustment expense is the cost of investigating, settling, and defending claims. It splits into allocated LAE (ALAE, tied to specific claims) and unallocated LAE (ULAE, general overhead like claims-department salaries).
- Loss Development
- Loss development is the emergence of losses through reporting, payment, and case-reserve adjustment over time after the accident period. The pattern is captured in loss triangles and projected via age-to-age factors.
- Loss Triangle
- A loss triangle is a matrix of cumulative paid or incurred losses by accident year (rows) and development period (columns). It is the canonical input to chain-ladder and other reserving methods.
- Loss Reserve
- A loss reserve is the liability recorded for unpaid losses. It includes case reserves (estimates for known claims) and IBNR (estimates for unreported claims and unanticipated development on known claims).
P
- Per-Risk Excess Reinsurance
- Per-risk excess reinsurance attaches on individual risk losses rather than per occurrence. It is common in property lines where loss can be concentrated in single risks (large factories, commercial real estate).
- Pricing Loadings
- Pricing loadings are the expense, profit, and contingency adjustments added to pure premium to derive the gross premium. They reflect the cost of capital, operating expenses, and the cost of bearing parameter and process risk.
- Pure premium is the expected loss per exposure unit. It is the loss component of the gross premium and the central quantity that ratemaking attempts to estimate accurately.
Q
- Quota share reinsurance is proportional reinsurance in which the reinsurer accepts a fixed percentage of every risk subject to the treaty. It provides capacity but does not protect against severity directly (the cedant retains the proportional share of each loss).
R
- Rate Filing
- A rate filing is the regulatory submission required in most US property-casualty lines that explains and supports a proposed rate change. It is reviewed and may be approved, disapproved, or modified by state insurance departments.
- A reinstatement premium is the additional premium paid to restore the limit of an excess reinsurance contract after a covered loss has exhausted a layer. It is typically a pro-rata portion of the original premium.
- Reserving Risk
- Reserving risk is the risk that ultimate loss costs differ from booked reserve estimates. It is a major source of property-casualty earnings volatility and a focus of regulatory capital requirements.
S
- Stop-Loss Reinsurance
- Stop-loss reinsurance is aggregate excess reinsurance covering the cedant's losses above an annual retention. It protects against unusual annual loss accumulation rather than against individual large losses.
T
- Tail Factor
- A tail factor is the development factor applied beyond the observable loss triangle to project losses to ultimate. It is estimated from industry data, curve fitting, or judgment when older accident years are not fully developed.
U
- Underwriting Cycle
- The underwriting cycle is the cyclical movement in pricing, profitability, and capacity in property-casualty markets. Hard markets feature rising prices and tight capacity; soft markets feature falling prices and abundant capacity.