Choice under uncertainty
§1. Expected utility (EU)¶
\(\succeq\) over lotteries¶
Preference axioms¶
EU Representation¶
Interpretation¶
§2. Risk aversion¶
vNM utility function¶
\[\begin{equation*}
U(F) = \int u(x) d F(x)
\end{equation*}\]
Absolute risk aversion¶
TBD
More risk-averse¶
TBD
CARA and additive risks¶
\begin{equation*}
u(x) = - e^{-ax}
\end{equation*}
CRRA and proportional risks¶
\[\begin{equation*}
u(x) =
\begin{cases}
\frac{x^{1-r}}{1-r} & \text{if } r \neq 1 \\
\ln x & \text{if } r = 1
\end{cases}
\end{equation*}\]