| 等级依赖效用下最优投资问题的扩展研究 |
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| 引用本文： | 罗马.等级依赖效用下最优投资问题的扩展研究[J].数学进展,2020(1):115-127. |
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| 作者姓名： | 罗马 |
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| 作者单位： | 北京航空航天大学数学与系统科学学院 |
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| 基金项目： | 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)。 |
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| 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.
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| 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 |
Extended Research on the Optimal Investment Problem with Rank-dependent Utility |
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| LUO Ma.Extended Research on the Optimal Investment Problem with Rank-dependent Utility[J].Advances in Mathematics,2020(1):115-127. |
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| Authors: | LUO Ma |
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| Institution: | (School of Mathematics and System Sciences,Beijing University of Aeronautics and Astronautics,Beijing,100191,P.R.China) |
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| Abstract: | 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. |
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| Keywords: | rank-dependent utility risk constraint probability weighting function nonsmooth generalized inverse function super-differential |
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