Obviously Bernoulli's assumption does not always hold. If we as individuals are better off paying comparatively small, fixed amounts at regular intervals (as an insurance premium) than risking a large loss, how is the insurance company better off by accepting these small amounts, and agreeing to risk a large loss? If buyers of insurance are indeed risk-averse - what about those who sell it? If it's logical for people to buy insurance, how come it's also logical to sell it? After all, insurance companies are in the business to make a profit. The rationale is straightforward - even though the probability of losing or damaging the item insured may be small, the potential loss would be so huge, that most people would rather pay moderate amounts of money for certain, than lose a large sum with a very small probability.īut there's another side to this - the insurance companies. This does seem like a reasonable assumption at first glance.īut is this always true? Most of us buy insurance - for cars, homes, and pretty much anything we consider valuable. Bernoulli assumed this would hold, since most people are risk-averse - they prefer a more certain outcome to a less certain one. In Bernoulli's formulation, this function was a logarithmic function, which is strictly concave, so that the decision-maker's expected utility from a gamble was less than its expected value. u(a i), is the Bernoulli utility function. Where the utility function over the outcomes, i.e. So an expected utility function over a gamble g takes the form: In the previous section, we introduced the concept of an expected utility function, and stated how people maximize their expected utility when faced with a decision involving outcomes with known probabilities.
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