Stochastic Dominance under the Nonlinear Expected Utilities

In 1947, von Neumann and Morgenstern introduced the well-known expected utility and the related axiomatic system (see von Neumann and Morgenstern (1953)). It is widely used in economics, for example, financial economics. But the well-known Allais paradox (see Allais (1979)) shows that the linear expected utility has some limitations sometimes. Because of this, Peng proposed a concept of nonlinear expected utility (see Peng (2005)). In this paper we propose a concept of stochastic dominance under the nonlinear expected utilities. We give sufficient conditions on which a random choice stochastically dominates a random choice under the nonlinear expected utilities. We also provide sufficient conditions on which a random choice strictly stochastically dominates a random choice under the sublinear expected utilities.