In economics exponential utility refers to a specific form of the utility function, used in many contexts because of its convenience when uncertainty is present. Economics is the social science that studies the production distribution, and consumption of goods and services. In Economics, utility is a measure of the relative satisfaction from or desirability of Consumption of various Goods and services. Uncertainty is a term used in subtly different ways in a number of fields including Philosophy, Statistics, Economics, Finance, Insurance Formally, exponential utility is given by:

u(c) = − e ac,

where c is consumption and a is a constant.

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

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

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. Risk aversion is a concept in Economics, Finance, and Psychology related to the behaviour of consumers and investors under uncertainty Risk aversion is a concept in Economics, Finance, and Psychology related to the behaviour of consumers and investors under uncertainty Specifically, under exponential utility, expected utility is given by:

E(u(c)) = E( − e a(c + ε)),

where E is the expectation operator. In Economics, Game theory, and Decision theory the expected utility theorem or expected utility hypothesis predicts that the "betting preferences" With normally distributed noise, ie,

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

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

$E(e^{-a \epsilon})=e^{-a \mu + \frac{a^2}{2}\sigma^2}.$
The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields
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