具有倍乘单次转换特性的效用函数研究  

Multiplicative One-switch Utility Functions

作　　者：张甲 谢杰华 邹娓[2] 马志鹏 ZHANG Jia;XIE Jiehua;ZOU Wei;MA Zhipeng(School of Business Administration,Nanchang Institute of Technology,Nanchang 330099,China;School of Science,Nanchang Institute of Technology,Nanchang 330099,China)

机构地区：[1]南昌工程学院工商管理学院,江西南昌330099 [2]南昌工程学院理学院,江西南昌330099

出　　处：《运筹与管理》2024年第5期140-146,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(72271113);江西省杰出青年科学基金项目(20202ACB211001);江西省研究生创新专项资金项目(YC2022-s979)。

摘　　要：在金融经济学和决策科学中,效用函数是描述决策者风险态度或满意程度最重要的理论工具之一,它也是风险和不确定性决策分析的基本工具。对效用函数特征和应用背景的研究一直是决策科学和风险管理领域的重要问题。本文提出了效用理论中的倍乘单次转换的概念,得到了具有倍乘单次转换特性的效用函数的四种具体形式,并且给出了它们与风险厌恶以及风险一致性之间的关系,从而为具有此特性的效用函数提供了实际的应用背景。以此为基础,本文进一步提出了倍乘强单次转换的概念,并证明了满足此特性的效用函数的具体形式。本文的研究丰富了效用理论中单次转换效用函数的研究内容,为分析具有倍乘单次转换特性的决策问题提供了理论工具。In financial economics and decision science,the utility function is one of the most important theoretical tools to describe the risk attitudes or the satisfaction degrees of individual decision makers,and it is also a basic tool for the decision analysis under risk and uncertainty.The research on the characteristic and properties of utility functions has been an important issue in the field of decision science and risk management.Under the framework of the expected utility theory,for any two lotteries,when the preference of the decision maker does not change as the wealth in these two lotteries increases,the forms of utility functions will be given explicitly.However,in reality,a decision maker could change his/her preference when the wealth in these two lotteries increases.Hence,the concept of one-switch in the utility theory is introduced,that is,a decision maker can change his/her preference for any two lotteries once at most as the wealth in these two lotteries increases.Meanwhile,the forms of one-switch utility functions are identified explicitly.It is a natural task to consider the notation of multiplicative one-switch corresponding to the characteristic,of which a decision maker can change his/her preference for any two lotteries once at most when the wealth in these two lotteries is multiplied by the same amount.To the best of our knowledge,there is little literature tackling this problem.Our objective is to fill the gap and shed some light on the study of this problem.Under the expected utility framework,the concept of multiplicative one-switch in the utility theory is introduced,that is,a decision maker can change his/her preference for any two lotteries once at most when the wealth in these two lotteries is multiplied by the same amount.The four forms of multiplicative one-switch utility function are obtained explicitly.They are the quadratic function of logarithm,the logarithm times power function,the power plus power function and the logarithm plus power function.Then,a wealth of relationship among t

关 键 词：效用函数 倍乘单次转换 相对风险厌恶系数 倍乘强单次转换 

分 类 号：C934[经济管理—管理学]