Disparity, shortfall, and twice-endogenous HARA utility

We derive a mapping between the shortfall-minimizing portfolio selection based on higher-order entropy measures and expected utility theory. We show that the family of HARA utility functions has a minimum-divergence, shortfall-based representation. This facilitates an interpretation in which the risk aversion parameters and the type of risk aversion arise endogenously. We provide a numerical example illustrating this interpretation.