Insurance Principles and Terminology

Before any formula matters, an actuary must be precise about what is being counted, over what period, and using what definition of a claim. This article is a working glossary of the terms that appear in every ratemaking and reserving conversation.

Exposure

Exposure is the basic unit of risk being insured — the denominator against which premium and loss are measured. Examples: car-years for personal auto, per $100 of payroll for workers' compensation, per $1,000 of building value for property. Exposure must be additive and proportional to expected loss for rate relativities to be meaningful.

Premium

Written premium is the full contractual premium recorded when a policy is issued or renewed. Earned premium is the portion of written premium "used up" as the policy period elapses — for a 12-month policy written on July 1, half is earned by December 31 of that year. Unearned premium is the remaining liability the insurer holds for future coverage. The earned premium is the correct denominator for a loss ratio because it is matched to the period of risk actually borne.

Loss, LAE, ALAE, ULAE

Loss is the amount paid or reserved for claims. LAE (loss adjustment expense) is the cost of investigating and settling claims, split into:

• ALAE (allocated LAE): assignable to a specific claim (defense counsel fees, independent medical exams). Often combined with loss for ratemaking ("loss and ALAE").
• ULAE (unallocated LAE): claims department overhead not assignable to a single claim (adjuster salaries), usually loaded as a percentage of loss and ALAE.

IBNR and IBNER

IBNR (incurred but not reported) is the reserve for claims that have happened but have not yet been reported to the insurer. IBNER (incurred but not enough reported, or "IBNR on known claims" / development on known claims) captures the expected future change in reserves on claims already reported — case reserves that will develop upward or downward as more information emerges. Total incurred losses are:

$\text{Incurred} = \text{Paid to date} + \text{Case reserves} + \text{IBNR (pure + IBNER)}.$

Many practitioners use "IBNR" loosely to mean the entire bulk reserve (pure IBNR + IBNER); precise usage separates the two because they have different drivers (reporting lags vs. case-reserving practices).

Accident year, policy year, report year, calendar year

These four "year" conventions organize the same underlying claims into different groupings, and confusing them is one of the most common actuarial errors:

• Accident year (AY): all claims from accidents/occurrences happening in a given calendar year, regardless of when the policy was written or the claim reported. AY data is the most common basis for ratemaking and reserving triangles because it aligns with when the exposure to loss occurred.
• Policy year (PY): all claims (and premium) from policies written (incepting) in a given year, tracked over the full life of those policies (which may extend claims 24 months beyond the AY equivalent for annual policies). PY is cleaner for evaluating a specific book of business/rate level but is slower to fully develop.
• Report year (RY): all claims reported to the insurer in a given year, regardless of accident date — used heavily in claims-made lines (e.g., medical malpractice, D&O) where the reporting date, not the occurrence date, triggers coverage.
• Calendar year (CY): all financial transactions (paid losses, reserve changes) recorded in a given calendar year regardless of the accident date of the underlying claim — this is the basis for statutory financial statements (Schedule P calendar-year figures) and is not directly usable for ratemaking without adjustment, since it mixes development from many accident years.

Loss ratio and combined ratio

The loss ratio is incurred losses (often plus ALAE) divided by earned premium: $LR = L/EP$. The combined ratio adds the expense ratio: $CR = LR + \text{Expense Ratio}$, where the expense ratio is underwriting expenses (commission, general expense, taxes) divided by written or earned premium depending on convention. A combined ratio below 100% indicates an underwriting profit before investment income; above 100% indicates an underwriting loss that must be offset by investment income to be profitable overall.

Worked example

A workers' compensation book has calendar-year 2023 earned premium of $40.0M, calendar-year paid losses of $18.0M, a calendar-year case reserve increase of $6.5M, an actuarial IBNR estimate of $3.0M (increase during the year), ALAE paid and reserved of $2.5M, and underwriting expenses of $9.6M.

Incurred losses = Paid + Case reserve change + IBNR change = $18.0M + $6.5M + $3.0M = $27.5M (losses only). Adding ALAE of $2.5M gives incurred loss & ALAE = $30.0M.

Loss ratio = $30.0M / $40.0M = 75.0%.

Expense ratio = $9.6M / $40.0M = 24.0%.

Combined ratio = 75.0% + 24.0% = 99.0% — a slight underwriting profit before investment income.

Pitfalls

• Using calendar-year incurred losses in a rate indication without recognizing they mix multiple accident years' development — the indication should be built on accident-year (or policy-year) triangles evaluated consistently.
• Mixing loss ratio denominators (written vs. earned premium) between numerator and denominator periods.
• Treating IBNR as a single number with one driver when pure IBNR (unreported claims) and IBNER (development on known claims) can move in opposite directions, e.g., after a claims-department initiative to close old files.
• Forgetting ALAE conventions differ by company — some report loss and ALAE combined, others net of a large-loss cap; always check the data dictionary.

Exam relevance

This terminology is foundational to CAS Exams 5, 6, 7, 8, and 9 and to SOA Exam GIFRE/FAM (general insurance track) — nearly every exam question assumes fluency with these definitions without redefining them.