Houjun Liu

power utility

power utility, or isoelastic utility, is a financial econometric is a utility that results absolute, constant relative risk aversion. i.e.: you tell me how risk averse you are exogenously, I tell you how much utility some consumption is.


  • some relative risk coefficient \(\gamma \in (0,1)\), higher more risk averse
  • consumption of some asset \(C\)


Utility \(U( C)\) is defined by:

\begin{equation} U( C) = \frac{c^{1-\gamma}-1}{1-\gamma} \end{equation}

additional information

As you can see, the higher \(\gamma\), the lower utility some consumption brings.

log utility

log utility is a special case of power utility whereby:

\begin{equation} U(x) = \log x \end{equation}

which converges to power utility where \(\lambda \to 1\).