Exponential Utility Function for different risk profiles
In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present, in which case expected utility is maximized. Formally, exponential utility is given by:
is a variable that the economic decision-maker prefers more of, such as consumption, and is a constant that represents the degree of risk preference ( for risk aversion, for risk-neutrality, or for risk-seeking). In situations where only risk aversion is allowed, the formula is often simplified to .
Note that the additive term 1 in the above function is mathematically irrelevant and is (sometimes) included only for the aesthetic feature that it keeps the range of the function between zero and one over the domain of non-negative values for c. The reason for its irrelevance is that maximizing the expected value of utility gives the same result for the choice variable as does maximizing the expected value of ; since expected values of utility (as opposed to the utility function itself) are interpreted ordinally instead of cardinally, the range and sign of the expected utility values are of no significance.
The exponential utility function is a special case of the hyperbolic absolute risk aversion utility functions.
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