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Risk aversion and utility

February 27, 2012

We can think of risk aversion in the context of utility. The most intuitive way is to consider wealth. Most of us would probably have a utility function that increases with diminishing returns as wealth increases. That is, the more wealth we have, the more utility we get (the happier we are), but the increases in our utility are greatest when we have less wealth. If you have wealth of nothing, and somebody offers you £10000, you are probably going to get a great deal of additional happiness from that £10000. However if you are already a multi-millionaire, then an extra £10000 might increase your happiness but it won’t have the same effect as it would if you had nothing.

A risk averse person will have a utility function relative to wealth, that looks similar to this:

A risk neutral person will have a utility function that looks like this:

A risk loving person will have a utility function that looks like this:

The shapes of the utility functions reflect the extent to which utility increases with wealth. The one of most interest to us is the risk averse one, because people are more likely to be risk-averse than anything else. This brings us to the concept of risk premium and insurance.

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