Abstract
In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We then introduce the moment rule and establish the necessary and/or sufficient conditions between stochastic dominance and the moment rule for the general utility functions and the polynomial utility functions of both risk averters and risk seekers with and without the same-location-scale-family condition. Thereafter, we apply the moment rules to develop some properties of portfolio diversification for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. The extensions in our paper enable academics and practitioners to draw preferences of both risk averters and risk seekers on their choices of the portfolios or assets by using different moments.
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