Utility and Risk Aversion

When asked, most people would prefer a payment of 1 billion US$ to a lottery that gives them either 2 billion US$ or nothing, both with a chance of 50%.

This is rational choice, if you appreciate that the difference in utility between having nothing and having a billion dollars is actually quite large, while it does not matter as much, whether one person owns one or two billion dollars. They are vastly rich in both cases.

The personal utility lost when giving away the first billion outweighs the personal utility gained by the transition from US$ 1 bill. to  US$ 2 bill.

While the expected value of the lottery equals 1 billion dollars, the expected utility is lower than the utility of the risk-free payment. This behavior is known as risk aversion.

It follows that a person who bears financial risk – depending on his personal risk aversion – can increase his utility by buying insurance against the risk, even if the insurance company charges considerably more than the expected cost and makes good profit.

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