Foundations of Risk & the Actuarial Profession

the concept of insurance

Most of us could not write a 300,000-dollar cheque tomorrow if our home burned down — yet the chance of that happening this year is small. Insurance is the deal that lets you trade that rare, unbearable possibility for a small, certain cost you can plan around. You pay a modest premium; in return, a company promises that if the named misfortune strikes, it will pay. You are, in effect, swapping a frightening maybe for a manageable definitely.

Insurance is a contract in which many people each pay a relatively small, certain premium into a common fund, and the few who actually suffer a covered loss are paid out of that fund. It rests on risk pooling and the law of large numbers: because the insurer covers a large group, the total it must pay each year is far more predictable than any one member's loss, so a steady premium can cover the lumpy claims. A simple shape: if 1,000 people each have a 1-in-100 chance of a 20,000-dollar loss, expected claims are about 200,000 dollars, so a premium near 200 dollars each (plus a margin for expenses and bad years) funds the promise. The customer values the certainty more than the small cost; the insurer profits by managing the pool well.

Insurance shows up everywhere actuaries work — life, health, property, liability, pensions, and reinsurance — but it has firm boundaries. It indemnifies, meaning it aims to restore a loss, not to enrich; it covers pure risk, not bets; and it relies on careful pricing, reserving, and capital so the promise is still good when claims arrive. A useful corrective: an insurer is not a savings account or a charity. Your premium is the price of a shared promise, and in most years most people pay more than they get back — that quiet majority is exactly what funds the unlucky few.

You pay 800 dollars a year for home insurance and, for twenty years, never claim — paying 16,000 dollars for 'nothing.' In year 21 a kitchen fire causes 120,000 dollars of damage and the insurer pays. The premiums of the many quiet years, yours and your neighbours', funded that one large payout.

The premiums of the many lucky years fund the rare large loss — that is the whole bargain.

Paying premiums for years without a claim is not 'wasted money' — it is the price of having been protected, and it is precisely what was available to pay the neighbours who did suffer a loss.

Also called
insuranceindemnity保险保障