New development on the third-order stochastic dominance for risk-averse and risk-seeking investors with application in risk management

Abstract

This paper develops new financial theory to link the third-order stochastic dominance (TSD) for risk-averse and risk-seeking investors and provide illustration of application in risk management. We present some interesting new properties of TSD for risk-averse and risk-seeking investors. We show that the means of the assets being compared should be included in the definition of TSD for both investor types. We also derive the conditions on the variance order of two assets with equal means for both investor types and extend the second-order SD reversal result of Levy and Levy (Manag Sci 48(10):1334–1349, 2002) to TSD. We apply our results to analyze the investment behaviors on traditional stocks and internet stocks for both risk averters and risk seekers.