Abstract
We propose a novel linear approximation of expected utility. The approximation guides us as we transfer the traditional quadratic dependence of third-order stochastic dominance (TSD) into an equivalent linear system. The finding also shows a dual relationship between traditional low partial moment condition and the efficient condition of Post (2003). Based on the transformation, we develop a linear algorithm of TSD. Furthermore, we refine the superconvex TSD of Post and Kopa (2017) and introduce a corresponding linear system. The portfolio optimization performances of various criteria are also investigated.
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