relative security (premium) loading

Charging customers exactly what their claims are expected to cost sounds fair, but it leaves no slack — one bad streak and the insurer is underwater. So insurers add a little extra on top of the expected cost, a deliberate cushion baked into the premium. The relative security loading is the size of that extra, expressed as a fraction of the expected claims: a 20 percent loading means you charge 20 percent more than break-even.

Precisely, if expected claims per unit time cost an amount we will call the pure premium rate, then the premium income rate c is set to c = (1 + theta) times that expected claims rate, where theta (often written as the Greek letter theta) is the relative security loading. So theta = 0 means charging exactly the expected claims (no cushion), theta = 0.2 means a 20 percent margin. The condition theta > 0, called the net profit condition, is exactly what gives the surplus an upward drift and stops ruin from being a certainty. For instance, if expected claims are 1,000,000 per year and theta = 0.15, then c = 1.15 * 1,000,000 = 1,150,000 per year.

The loading is the single most important dial in ruin theory. A bigger theta steepens the upward drift of surplus and sharply lowers the probability of ruin; it also raises the adjustment coefficient, tightening the Lundberg bound. But theta cannot be set freely — competition pushes it down, and customers shop on price. The actuary's job is to find a loading large enough for solvency yet small enough to stay competitive. Note that the security loading is not the only loading in a real premium: gross premiums also carry expense and profit loadings, which are separate ideas; theta here is purely the margin protecting against random claim fluctuation.