An insured individual makes payments called "premiums" to an insurer, and then in return is able to claim a payment from the insurer if the insured has suffered a defined type of loss. This agreement is normally drawn up in a legal contract, which is also known as a policy. The contract set's out in detail the precise circumstances under which a payment will be made and the amount payed in premiums.
For example, a ship owner insures his ship and receives a payment if the ship is damaged / destroyed. This was one of the earliest uses and developments of a concept like insurance.
Insurance companies will attempt to quantify risk by pooling together a large number of risks. This uses the law of large numbers. For insurance, the greater the number of similar risks, insurers can estimate overall risk with greater accuracy.
E.g., when individuals purchase a health insurance policies they pay an large monthly or yearly premium to the insurance company. If a policyholder gets ill, the insurance company will provide the money to cover medical treatment. For some the insurance benefits may be far more money than they ever paid into the policy, whilst others may never make a claim. The claims will even out when the payout's are averaged out over all of the policies. Insurance companies will set these premiums based on their calculated payouts. They intend to take in more money than they pay out to cover expenses. Insurance companies intent on profit will set their rates to make a profit rather than to break even.
Insurance companies will also earn investment profits, this is because they have the use of the money from premiums from the time they receive it until the time pay claims. This money is refered to as the float. When invested successful, they can earn large profits.
Insurance can also be thought of as a wager / bet over the policy period. The insurance company will bet that you or your property will not suffer a loss while you are putting money on the opposite outcome.
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