摘要
本文在文献[https://ssrn.com/abstract=3135695]的基础上,去掉了等级依赖效用投资者的概率加权函数的连续性和单调增加的严格性,以及其原始效用函数的连续可微性.通过引入一般单调函数的广义逆函数以及凹函数的超微分,克服了分析上所带来的新的困难,证明了新模型最优解的存在性并给出其显式表达.
Based on the literature [https://ssrn.com/abstract=3135695],this paper removes the continuity and the strictness of monotonous increase of the probability weighting function in the rank-dependent utility theory,as well as the continuous differentiability of the original utility function.By introducing the generalized inverse function of the general monotone function and the super-differential of the concave function,we will overcome the new difficulties in analysis,prove the existence of the optimal solution of the new model and give its explicit expression.
作者
罗马
LUO Ma(School of Mathematics and System Sciences,Beijing University of Aeronautics and Astronautics,Beijing,100191,P.R.China)
出处
《数学进展》
CSCD
北大核心
2020年第1期115-127,共13页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11801032)
中国科学院数学与系统科学研究院随机复杂结构与数据科学重点实验室资助(No.2008DP173182)。
关键词
等级依赖效用
风险约束
概率加权函数
非光滑
广义逆函数
超微分
rank-dependent utility
risk constraint
probability weighting function
nonsmooth
generalized inverse function
super-differential
