Lipschitz Bernoulli Utility Functions
本文在带或不带完备性公理的情况下，得到了冯·诺依曼-摩根斯坦期望效用定理的多个变体，其中导出的伯努利效用函数是利普希茨的。奖品空间是任意可分度量空间，效用函数允许无界。主要创新是一个新的行为公理，几乎所有随机序都满足它。
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.