运筹学学报2024,Vol.28Issue(1) :77-88.DOI:10.15960/j.cnki.issn.1007-6093.2024.01.006

基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究

The study of distributionally robust reward-risk optimization models with moment-based ambiguity set

李颖涵 童小娇 杨柳
运筹学学报2024,Vol.28Issue(1) :77-88.DOI:10.15960/j.cnki.issn.1007-6093.2024.01.006

基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究

The study of distributionally robust reward-risk optimization models with moment-based ambiguity set

李颖涵 1童小娇 2杨柳3
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作者信息

  • 1. 湖南师范大学数学与统计学院,湖南长沙 410081
  • 2. 湖南第一师范学院数学与统计学院,湖南长沙 410205
  • 3. 湘潭大学数学与计算科学学院,湖南湘潭 411105
  • 折叠

摘要

本文研究随机变量分布不确定下的风险-回报优化模型.针对传统的风险-回报三类典型问题和分布不确定性背景,提出了更一般性条件下的分布鲁棒风险-回报优化新模型;基于矩不确定集合和优化对偶理论,化简复杂的新优化模型为常规结构的非线性优化问题.理论上证明了分布鲁棒风险-回报三类优化模型效率前沿的等价性.数值实验验证了理论分析的有效性.

Abstract

This article studies the reward-risk optimization model under the uncer-tain distribution of random variables.In view of the three typical problems of traditional reward-risk and the background of uncertainty of distributions,a new model of distri-butionally robust reward-risk optimization is proposed under more general conditions.Based on moment ambiguity set and optimal duality theory,the complex new optimiza-tion model is simplified to a nonlinear optimization problem of conventional structure.The equivalence of efficient frontier of three types of distributionally robust reward-risk optimization models is proved theoretically.Numerical example verifies the effectiveness of the theoretical analysis.

关键词

风险-回报优化问题/分布鲁棒优化/效率前沿/鲁棒对应

Key words

reward-risk optimization problems/distributionally robust optimiza-tion/efficient frontier/robust counterpart

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基金项目

国家自然科学基金(12331011)

国家自然科学基金(12171145)

出版年

2024
运筹学学报
中国运筹学会

运筹学学报

CSTPCDCSCD北大核心
影响因子:0.25
ISSN:1007-6093
参考文献量21
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