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Mathematical Problems in Engineering
Volume 2014, Article ID 713738, 6 pages
http://dx.doi.org/10.1155/2014/713738
Research Article

Stochastic Dominance under the Nonlinear Expected Utilities

1Shandong University Qilu Securities Institute for Financial Studies and School of Mathematics, Jinan 250100, China
2School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China

Received 26 March 2014; Revised 28 May 2014; Accepted 19 June 2014; Published 31 August 2014

Academic Editor: Guangchen Wang

Copyright © 2014 Xinling Xiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.