= Concavification of incentive utility
{title2=$\bar F=\text{least concave majorant of }F$}
Concavification replaces a nonconcave incentive <utility function> by its least <concave majorant>. In a <complete market> with an atomless <state-price density>, the optimizing payoff may avoid all intervals where the majorant strictly exceeds the original utility, making the relaxed optimum exactly attainable. At a pricing atom corresponding to a linear segment, a lottery between contact points can attain the same value at unchanged cost.
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