Insurance deals in risks, not unknowns or certainties. There is a fine line between the two that is frequently misunderstood. A risk is an event whose probability you can calculate; an unknown is an event whose probability you cannot calculate; a certainty is, well, certain to occur.
We know for instance, with a statistically meaningful sample, that a certain percentage of the population dies or has a car accident each year. They follow near perfect gaussian distributions, and therefor are risks. You can price them appropriately and a private insurance take care of them.
From a mathematical standpoint, an insurance company's usefulness begins and ends here: guaussian distribution, large enough sample. This can be priced; nothing else can. Collecting an insurance coupon for anything else is gambling, leeching, or both -- and on the tax payer's back, more often than not.
Earthquakes or stock market moves, for instance, follow power laws, and therefor are unknowns. You cannot price them appropriately and a private insurance cannot credibly take them. When it does, you end up with lavish profits and dividends in good years (heads, I win), and State emergencies / AIGs in bad years (tails, you lose).
Health follows a power law too (diseases are contagious, health degrades with health issues) with the added twist of certainties (e.g., the majority of one's health care costs are concentrated in the last few years of one's life). These are unknowns and certainties, not risks. As such, they cannot be priced appropriately from an insurance's standpoint. For healthy people, the best an insurance can do is gamble (heads, I win); for the elderly or chronic diseases, it needs to price (or refuse to "insure") the inevitable (tails, you lose).
Yet other things, such as space flight accidents, might arguably follow gaussian distributions. They could be insured in theory -- if gaussian indeed. In practice however, the sample is too small to know the precise risk. Until it's larger, this risk cannot be adequately priced. And the best a private insurance can do is gamble. The insurance might over-price the risk and over-provision for catastrophes (heads, I win, tails, you win; yay!). It might also under-price the risk and distribute lavish dividends (heads, I win) and go bust when a space ship crashes into a nuclear power plant (tails, you lose). It simply lacks the data to take the appropriate decision; it's an unknow.
So the real question is: is the tax payer comfortable with someone winning on heads, without knowing if he'll win or lose on tails?
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