= Small multiplicative risk premium
{title2=$\psi\simeq\tfrac12\alpha(W)\operatorname{Var}(\phi)$}
Compare expected utility of $W(1+\phi)$, where $\mathbb E\phi=0$, with the certainty equivalent $W(1-\psi)$. A second-order <Taylor expansion> gives $U(W)+W^2U''(W)\mathbb E\phi^2/2$ for the risky side and $U(W)-WU'(W)\psi$ for the sure side. Equality gives the displayed proportional <risk premium>. This requires a genuinely small-shock family with controlled remainders; small variance alone does not control rare large wealth shocks.
Back to article page
