increased limits factors and deductible relativities
Two customers can buy the 'same' liability policy yet choose very different amounts of protection: one caps the insurer's payout at 100,000 dollars, another at 1,000,000; one takes a 500 deductible, another a 2,000. They should not pay the same price, because they are buying different slices of the same loss distribution. Increased limits factors and deductible relativities are the tools that price those choices.
An increased limits factor (ILF) is the multiplier that scales the premium for a basic limit up to a higher limit. Crucially, doubling the limit does not double the price, because most claims are small and only a few ever reach the upper layers. So the ILF from a 100,000 to a 1,000,000 limit might be only about 1.6, not 10. ILFs are built from the severity distribution: the factor equals the expected loss capped at the higher limit divided by the expected loss capped at the basic limit. Deductible relativities work the mirror-image way: choosing a higher deductible removes the small, frequent losses the insurer would have paid below it, so the premium drops. The discount is measured by the loss elimination ratio — the fraction of expected losses eliminated by the deductible. A 1,000 deductible that eliminates 12 percent of expected losses gives a relativity of about 0.88.
These factors are how a rating plan offers a menu of coverage from one underlying loss model, and they are deeply tied to the shape of the severity distribution — especially its tail. That is the catch: high limits are driven by rare, large claims where data is thin, so ILFs for very high limits rest heavily on fitted heavy-tailed distributions and judgment, and small changes in tail assumptions can move them a lot. Deductible relativities are usually steadier because they depend on the well-populated small-loss part of the distribution.
ILF from 100k to 1M limit ≈ 1.6 (not 10), because large claims are rare. A 1,000 deductible eliminating 12% of expected losses (loss elimination ratio 0.12) gives a deductible relativity of about 1 − 0.12 = 0.88.
Doubling a limit barely doubles price; a higher deductible cuts the frequent small losses.
Increased limits factors rest on the thin, uncertain tail of the severity distribution, so they are sensitive to tail assumptions. A common error is to assume the price rises linearly with the limit — it does not, because large losses are rare.