<p>This is trivially <strong>not</strong> true. Consider simple example of utility:</p>
<p><span class="math-container">$$u(x) = x^{1/2}$$</span></p>
<p>Expected utility <span class="math-container">$E(u(x)) = E[x^{1/2}]$</span></p>
<p>Inverse utility is <span class="math-container">$u^{-1} \implies x = u^2 $</span></p>
<p>clearly generally <span class="math-container">$E(u) \neq u^{-1} $</span>.</p>

CC BY-SA 4.0
2020-12-03T10:09:03.467Z
Why do you substitute the EU in the inverse of the utility funcciton to obtain the risk premium?
Teko JR
CC BY-SA 4.0
2020-12-03T10:16:17.420Z
@TekoJR I don’t know what you are talking about. In economic literature risk premium is commonly defined as the difference between expected payoff from gamble and its certainty equivalence of the same gamble or in more finance oriented literature as a difference between expected return on risky and riskless asset of the same kind.
1muflon1
CC BY-SA 4.0
2020-12-03T10:07:23.213Z
2020-12-03T10:56:31.867Z
2020-12-03T10:56:31.867Z
1muflon1
<p>Can somebody explain to me if that it's true and also graphically explain it?</p>

CC BY-SA 4.0
2020-12-03T09:45:53.617Z
No. It is not the inverse of the utility function. Why would you believe this?
Bayesian
<microeconomics><utility><expected-utility><measuring-utility>
Is the expected utility the inverse of the utility function?
Teko JR
# Is the expected utility the inverse of the utility function?

(Asked by: username_0 on 2020-12-03)

Can somebody explain to me if that it's true and also graphically explain it?

**Tags:** microeconomics, utility, expected-utility, measuring-utility

> **Comments:**
> **username_1**: No. It is not the inverse of the utility function. Why would you believe this?  

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## 1 answers

### Answer by username_2 on 2020-12-03. Score: 2

This is trivially **not** true. Consider simple example of utility:

$$u(x) = x^{1/2}$$

Expected utility $E(u(x)) = E[x^{1/2}]$

Inverse utility is $u^{-1} \implies x = u^2 $

clearly generally $E(u) \neq u^{-1} $.

> **Comments:**
> **username_0**: Why do you substitute the EU in the inverse of the utility funcciton to obtain the risk premium?  
> **username_2**: @username_0 I don’t know what you are talking about. In economic literature risk premium is commonly defined as the difference between expected payoff from gamble and its certainty equivalence of the same gamble or in more finance oriented literature as a difference between expected return on risky and riskless asset of the same kind.  

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