Uninsurable Peril

You can't call an insurance company to sign up for shark insurance just as the great white digs its teeth into your leg. That situation would represent an uninsurable peril.

In general, the term indicates a disastrous event that is both catastrophic (meaning expensive for the insurance company) and highly likely to happen. Basically, a claim is bound to happen sometime, so a policy would represent a sure loser for any insurance company.

You try to open a hot dog stand in Trafalgar Square and buy pigeon poop insurance. Another uninsurable peril. Your inventory is likely to get ruined one way or another.

Hurricane insurance in many areas works on this basis. It's excluded from many policies as an uninsurable peril, requiring governments to step in with supplemental programs.