The Fatal Conceit

Here is a bit more on insurance and states of nature.  In the language of economics a rational, utility maximizer allocates income to equate the marginal utility of income across all contingent-states.  Thus, a rational, utility maximizer moves income from states where the marginal utility is low to states where is high, e.g. home insurance moves money from the state in which your house doesn't burn and transfers it to the state in which your house does burn  - that's good because if your house burns the marginal utility of money will be high.  Usually, the marginal utility of money is high in the "bad" state but not always.  The classic case is that it's not generally a good idea to buy death insurance for your kids.  If your kids die you are going to be miserable and more money won't help much – better to not buy the insurance and take the kids to the movies.  Bertram and Dworkin are probably right that more money doesn't buy you much more utility if you are a vegetable, thus you don't want big transfers of income to this state.  Summarizing, the first notion of insurance is transferring money across states.

The second notion of insurance is using money to avoid the bad outcome.  It doesn't make sense to buy death insurance for your kids but it does make sense to buy them health insurance.  Similarly, you don't want to win the lottery when you are a vegetable but you might be williing to use lottery winnings to avoid becoming a vegetable.  

Arrow and especially Hirshleifer laid this all out in the 1960s.