pure premium
/ PYOOR PREE-mee-um /
Strip a price down to its bare bones: forget commissions, taxes, profit, and overhead. What is left is just the average claim cost the insurer expects to pay for one unit of insurance over one period. That bare cost is the pure premium. It is the price before any of the business expenses are bolted on.
Numerically, the pure premium is total expected losses divided by the number of exposures. An 'exposure' is the basic unit you charge by — one car-year of auto insurance, one 1,000 dollars of property value, one payroll dollar in workers' compensation. If 1,000 car-years generate 300,000 dollars of expected losses, the pure premium is 300 dollars per car-year. You can also build it from two pieces: frequency (claims per exposure) times severity (average cost per claim). If cars have a claim 5 percent of the time and the average claim is 6,000 dollars, the pure premium is 0.05 times 6,000 = 300 dollars. Same answer, built two ways.
The pure premium is the heart of the price; everything else is loaded on top to turn it into the premium a customer actually pays. It also lets actuaries compare risks cleanly. A young driver with a 600 dollar pure premium genuinely costs twice as much to insure as a driver with a 300 dollar pure premium, regardless of how expenses or profit are added. If loss adjustment expense is folded in, the result is usually called the loss cost rather than the pure premium.
Frequency 0.05 claims per car-year times severity 6,000 dollars per claim = a pure premium of 300 dollars per car-year, before any expense or profit loadings.
Pure premium = frequency × severity = expected losses ÷ exposures.
Pure premium is a cost per exposure, not a percentage. Do not confuse it with a loss ratio (losses as a fraction of premium); the two methods of rate indication differ precisely on which of these they use.