loss and premium trend
Prices in the world keep moving. A car repair that cost 4,000 dollars three years ago might cost 4,600 today; medical bills climb; and the mix of who buys insurance shifts too. So when an actuary uses last year's claims to price next year's policies, those old figures are stale. Trending is the adjustment that ages historical losses (and premium) forward to the cost levels of the future period the new rates will cover.
Loss trend is usually split into two parts. Frequency trend is the change in how often claims happen per exposure — safer cars and better roads may push it down, more cars on the road may push it up. Severity trend is the change in the average cost per claim, driven largely by inflation in repairs, medical care, wages, and jury awards. The total annual loss trend is roughly frequency trend plus severity trend. For example, if frequency is falling 2 percent a year and severity rising 5 percent, pure premium is trending up about 3 percent a year; projecting two and a half years forward multiplies losses by 1.03 to the 2.5 power ≈ 1.077. Premium is trended too, mainly to reflect drift in the average amount of insurance bought (for instance, rising property values raise premium even with no rate change).
Trend is one of the most judgment-laden and consequential steps in ratemaking, because a small error compounds over the years between the data and the future policy period. Actuaries fit trends to internal data and external indices (inflation, repair-cost surveys), but must beware that recent inflation spikes, COVID-era distortions, or law changes can break a smooth historical trend. A flat extrapolation of a temporary spike — or ignoring a real regime change — is a classic way to get the price badly wrong.
Frequency trend −2% per year, severity trend +5% per year, so pure-premium trend ≈ +3% per year. To project losses 2.5 years from the data midpoint to the future policy period: multiply by 1.03^2.5 ≈ 1.077.
Loss trend ≈ frequency trend + severity trend, compounded over the projection period.
Trend and loss development are different adjustments and must not be double-counted: development moves a known accident period's losses to their ultimate value; trend moves cost levels from one period to a later period. Mixing them up inflates the price twice.