风险决策中展望空间上非线性效用表示的存在性

Representations of nonlinear functions on prospect spaces in risk decision-making

效用理论是风险决策理论的重要组成部分,它可划分为线性效用理论和非线性效用理论．线性效用是一种较为极端的情形;其存在性已由Von Neumann和O Morgenstern于1944年解决．因而,余下的最主要的也是最困难的问题是解决非线性效用的存在性及相关应用．对此作了一些探讨,给出了三个非线性效用表示的存在性定理．

Nonlinear representations on prospect spaces in nsk decision-making are further discussed, and three creative results are obtained. These results are independent of each other and new theorems of the existence of nonlinear representations on prospect spaces are given out.