$u(c)=-e^\{-a\; c\}$,

where $c$ is consumption and $a$ is a constant.

Exponential utility implies constant absolute risk aversion, with coefficient of absolute risk aversion equal to

$frac\{-u\text{'}\text{'}(c)\}\{u\text{'}(c)\}=a.$

Though isoelastic utility, exhibiting constant relative risk aversion, is considered more plausible (as are other utility functions exhibiting decreasing absolute risk aversion), exponential utility is particularly convenient for many calculations. Specifically, under exponential utility, expected utility is given by:

$E(u(c))=E(-e^\{-a\; (c+epsilon)\}),$

where E is the expectation operator. With normally distributed noise, ie,

$epsilon\; sim\; N(mu,\; sigma^2),!$

E(u(c)) can be calculated easily using the fact that

$E(e^\{-a\; epsilon\})=e^\{-a\; mu\; +\; frac\{a^2\}\{2\}sigma^2\}.$