Lipschitz Bernoulli Utility Functions

• 成果类型: Article
• 署名作者: Ok, Efe A.; Weaver, Nik
• 署名单位: New York University; New York University; Washington University (WUSTL)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1270
• 发表日期: 2023
• 页码: 728-747
• 关键词: expected utility; completeness; differentiability; preferences

摘要

We obtain several variants of the classic von Neumann-Morgenstern expected utility theorem with and without the completeness axiom in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary separable metric space, and the utility functions are allowed to be unbounded. The main ingredient of our results is a novel (behavioral) axiom on the underlying preference relations, which is satisfied by virtually all stochastic orders. The proof of the main representation theorem is built on the fact that the dual of the Kantorovich-Rubinstein space is (isometrically isomorphic to) the Banach space of Lipschitz functions that vanish at a fixed point. An application to the theory of nonexpected utility is also provided.