Ratemaking, Loss Reserving, and Actuarial Concepts
Ratemaking principles
Rates must be adequate, not excessive, and not unfairly discriminatory. The pure premium method builds a rate from loss cost plus a loading for expenses, profit, and contingencies; the loss ratio method adjusts current rates by the ratio of actual to expected loss ratios. Trend, development, and credibility adjustments are applied before rates are finalized. A frequent trap is forgetting that trend and development are separate: trend projects future severity and frequency, development corrects for losses not yet reported or paid.
Reserving methods
Loss reserves are estimates of unpaid claims, split into case reserves (specific claims) and incurred but not reported (IBNR) reserves. Methods include chain-ladder development, expected loss ratio, Bornhuetter-Ferguson (blends expected loss ratio with reported development), and frequency-severity. The actuarial reserve is the central estimate; ranges reflect uncertainty. Reserve adequacy is judged against subsequent development.
Key concepts
Credibility weighs the volume of data: limited data means more reliance on external benchmarks. Loss development factors convert reported losses at a maturity to ultimate. Discounting recognizes time value but is limited in statutory reporting. Catastrophe loads and reinsurance costs affect the final rate.
Worked example
A chain-ladder age-to-ultimate factor of 1.25 applied to $4M of reported losses gives $5M ultimate, so IBNR is $1M. Rule of thumb: ultimate = reported x development factor; IBNR = ultimate minus reported minus case reserves already held. Always check that the factor direction increases losses for immature years and approaches 1.0 as the year matures.