coinsurance factor
Even after you have paid a deductible, many policies do not refund 100% of the remaining loss — they pay a fixed percentage, say 80%, and leave the other 20% to you. That percentage the insurer pays is the coinsurance factor. It keeps you sharing in every loss, large or small, so you stay motivated to avoid and minimise claims.
If the coinsurance factor is alpha (a number between 0 and 1, often written as 80%), the insurer multiplies its share by alpha. In the simplest case with no deductible or limit, a loss X produces a payment of alpha times X — an 80% coinsurance on a 10,000 loss pays 8,000, with 2,000 borne by the insured. In a full layered policy the order is: take the loss, subtract the ordinary deductible, apply coinsurance to what remains, and then cap at the limit, giving alpha times (min(X, u) - d) for losses above d. The factor scales the whole payment proportionally, top to bottom.
Coinsurance is a core lever in health insurance (where you might pay 20% of medical bills after a deductible) and in commercial property. Its purpose is partly cost control and partly behaviour: because the insured always keeps a slice, the incentive to over-treat or over-claim is dampened. Two clarifications matter. First, health-insurance 'coinsurance' (your share of each bill) is a different idea from property-insurance 'coinsurance clauses' that penalise underinsurance relative to value — same word, different mechanics. Second, coinsurance is not the same as a deductible: a deductible removes a fixed bottom amount, while coinsurance takes a constant fraction of whatever is left, so it bites on big claims too.
A health plan has a 1,000 deductible and 80% coinsurance, with an out-of-pocket maximum aside. On a 6,000 bill: you pay the first 1,000, then 20% of the remaining 5,000 (that is 1,000), so you pay 2,000 and the insurer pays 4,000 — the insurer's share is 0.80 times (6,000 - 1,000) = 4,000.
Insurer pays a fixed fraction (alpha) of the loss left after the deductible — sharing every claim.
Health-plan coinsurance (your percentage of each bill) is not the same as a property 'coinsurance clause', which penalises you for insuring a building below a required fraction of its value. The word is shared; the mechanics are not.