Duality of Shortfall Aversion

This study constructs a dual framework for a class of utility functions with or without discounting, without using the HJB method commonly employed in the literature to determine local optimality. The study shows that shortfall aversion can be directly incorporated into the dual problem through a singular control mechanism characterized by variational inequalities, and the resulting value function strictly outperforms existing literature results. This framework treats consumption peaks as an independent non-decreasing control and determines their optimal evolution through duality, providing a more general and flexible analytical framework for consumption optimization under shortfall aversion.