= Complete-market terminal utility optimizer
{title2=$X^*=I(y\zeta)$}
For an increasing strictly concave <utility function> satisfying the <Inada conditions>, put $I=(U')^{-1}$ and let $\zeta$ be the positive terminal <state-price density>. In a finite complete market, select $y>0$ so that $\mathbb E[\zeta I(y\zeta)]$ equals initial wealth. The displayed payoff is optimal under that budget: the supporting-line inequality for utility has marginal slope $y\zeta$, and its expected linear error vanishes on the budget constraint. <Market completeness> supplies its replicating strategy.
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