Effi cient Diversification under Generalized Almost Stochastic Dominance

Stochastic dominance (SD) has been identified as an important method for effi cient diversification. However, the SD rule is too rigid in that it remains silent on some obvious preferences between two distributions for most investors as pointed out by Leshno and Levy (2002). Thus the purpose of this paper is to derive an effi cient frontier according to generalized almost stochastic dominance (GASD) rules proposed by Tsetlin et al. (2015), which can effectively delete the choices which are not preferred by most economically important decision makers. We first respectively propose tests for portfolio admissibility and portfolio optimality under generalized almost first-degree stochastic dominance. We then propose tests for effi cient diversification under generalized almost second-degree stochastic dominance. In each test, we demonstrate how to use computational and tractable linear programming to implement the tests and provide their applications in the stock markets.