= Floored marginal utility optimizer
{title2=$w_T^*=\max\{\xi,I(\lambda\zeta_T)\}$}
For a nonnegative <terminal wealth floor> whose <state-price density> cost is strictly below the available budget, pointwise maximization of $U(y)-\lambda\zeta_Ty$ over $y\geq\xi$ gives the displayed payoff. The positive multiplier exhausts the <state-price budget constraint>. This requires the usual utility and integrability hypotheses ensuring that the multiplier exists and the payoff is replicable.
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