 Concavification of incentive utility

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.