Rationality

Is it wise to purchase insurance? For example, if I buy auto insurance, then I'm betting that I will be in an accident, and that the insurance payout will be worthwhile, notwithstanding the amount I will have paid in premiums. The insurance company is betting that the amount I pay in premiums will outweigh what they pay me in the event of a claim. Given that they have a lot of actuaries and other smart folks working on this, shouldn't I assume that they are right? I.e., does the fact that someone very smart is willing to sell me insurance count as a reason not to buy the insurance?

Comments

One buys insurance for any number of reasons, but the one to which you refer is to protect against a set of relatively improbable events, but events that should they happen would have a devastating effect upon you (or your next of kin!). We can define 'devastating' as meaning: having an effect that is of a different order to the effect of paying the premium. Because the insurance company deals in probabilities across millions of cases, the rationality of selling the policy is simply a mathematical calculation. But for an individual, the rationality involved it is not merely mathematics, but an appraisal of what is too valuable to risk. Thus, the insurance salesperson and I can both be 'smart'.

Suppose I pay a premium of $100 for accident insurance. I have an accident, and the hospital bills are $500,000. The odds against having such an accident are 10000 to 1. So, a good deal for the insurance company who, averaged across many thousands of policies, will make a profit. But also a good deal for me, since having to pay out $500,000 myself would have been devastating. I hardly noticed the premium, but the hospital bill would have ruined my life.

That is why we don't tend to insure small things: I wouldn't buy insurance against getting a cold because, in normal circumstances, that wouldn't be devastating in the above sense. But, we do insure things that are not terribly valuable in monetary terms, but whose loss would be devastating: family heirlooms, for instance, or indeed people. In such cases, the insurance payout is not intended to make things right, but to compensate for the loss.

Please also see the questions and answers gathered together under the topic Probability.

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