Jaehyun Kim et al. publish dual framework paper for shortfall aversion
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Jaehyun Kim and Hoi Ying Wong have published a research paper on a dual framework for shortfall aversion, covering multiple classes of utility functions with and without discounting, without relying on the commonly used HJB method to determine local optimality. The study proposes a singular control mechanism characterized by variational inequalities, which directly incorporates shortfall aversion into the dual problem, yielding a value function strictly superior to existing literature results. It also 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.
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- arXiv q-finDuality 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.
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