Stochastic Dominance under the Nonlinear Expected Utilities

Abstract EN

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 X stochastically dominates a random choice Y under the nonlinear expected utilities.

We also provide sufficient conditions on which a random choice X strictly stochastically dominates a random choice Y under the sublinear expected utilities.