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From the point of view of the insurance company there are four general criteria for deciding whether to insure events or not.

1. there must be a larger number of similar objects so the financial outcome of insuring the pool of exposures is predictable. Therefore they can calculate a "fair" premium.

2. the losses have to be accidental and unintentional from the point of view of the insured.

3. the losses must be measurable, identifiable in location, time, and be definite. They also want the losses to cause economic hardship. That is, so the insured has an incentive to protect and preserve the property to minimize the probability that the losses occur.

4. the loss potential to the insurer must be non-catastrophic. It cannot put the insurance company in financial jeopardy.

Losses must be uncertain.

The rate and distribution of losses must be predictable: To set premiums (prices) insurers must be able to estimate them accurately. This is done using the Law of Large Numbers which states that: The larger the number of homogenous exposures considered, the more closely the losses reported will equal the underlying probability of loss. If the coverage is unique, the insured will pay a correspondingly higher premium. Lloyd's of London often accepts unique coverages.

The loss must be significant: The legal principle of De minimis dictates that trivial matters are not covered. Furthermore, rational insurance uses existing insurance when the transaction costs dictate that filing a claim is not rational. Actually, De minimis does not come into play here. The reality is that it costs too much to insure frequent and/or small losses. It is much more cost effective to not transfer small loss potential to insurance companies by taking the largest deductible that you can stand (given adequate price reduction). As for filing small claims, if the insurance company contractually should pay for it, you should file it. This is the difference between deciding before the contract the parameters and after following through.

The loss must not be catastrophic: If the insurer is insolvent, it will be unable to pay the insured. In the United States, there is a system of Guarantee Funds that run at the state level to reimburse insured people whose insurance companies have become insolvent.
This program is run by the National Association of Insurance Commissioners (NAIC).
In the United Kingdom, the Financial Services Authority (FSA), which regulates all insurance companies, has its own standards of solvency which must, by law, be adhered to. To avoid catastrophic depletion of their own capital, insurers almost universally purchase reinsurance to protect them against excessively large accumulations of risk in a single area, and to protect them against large-scale catastrophes.

Additionally, “speculative risks” like those incurred through gambling or through the purchase of company stocks are uninsurable.

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