基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究

doi:10.15960/j.cnki.issn.1007-6093.2024.01.006

运筹学学报 ›› 2024, Vol. 28 ›› Issue (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

李颖涵¹, 童小娇²^,*(), 杨柳³

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

收稿日期:2021-09-08 出版日期:2024-03-15 发布日期:2024-03-15
通讯作者: 童小娇 E-mail:xjtong-csust@hotmail.com
基金资助:
国家自然科学基金(12331011);国家自然科学基金(12171145)

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

Yinghan LI¹, Xiaojiao TONG²^,*(), Liu YANG³

1. School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, Hunan, China
2. School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, Hunan, China
3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China

Received:2021-09-08 Online:2024-03-15 Published:2024-03-15
Contact: Xiaojiao TONG E-mail:xjtong-csust@hotmail.com

摘要/Abstract

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。

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

Abstract:

This article studies the reward-risk optimization model under the uncertain 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 distributionally robust reward-risk optimization is proposed under more general conditions. Based on moment ambiguity set and optimal duality theory, the complex new optimization 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.

Key words: reward-risk optimization problems, distributionally robust optimization, efficient frontier, robust counterpart

中图分类号:

O221.2

李颖涵, 童小娇, 杨柳. 基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究[J]. 运筹学学报, 2024, 28(1): 77-88.

Yinghan LI, Xiaojiao TONG, Liu YANG. The study of distributionally robust reward-risk optimization models with moment-based ambiguity set[J]. Operations Research Transactions, 2024, 28(1): 77-88.

图/表 5

参考文献 21

1	Tong X J , Wu F F . Robust reward-risk ratio optimization with application in allocation of generation asset[J]. Optimization, 2014, 63 (11): 1761- 1779. doi: 10.1080/02331934.2012.672419
2	Shapiro A , Dentcheva D , Ruszczynski A . Lectures on Stochastic Programming: Modeling and Theory[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2009.
3	Zhu S S , Fukushima M . Worst-case conditional value-at-risk with application to robust portlolio management[J]. Operations Research, 2009, 57 (5): 1155- 1168. doi: 10.1287/opre.1080.0684
4	Tong X J , Wu F , Qi L Q . Worst case CVaR based portfolio optimization models with applications to scenario planning[J]. Optimization Methods and Software, 2009, 24 (6): 933- 958. doi: 10.1080/10556780902865942
5	Markowise H M . Portfolio selection[J]. Finance, 1952, 7 (1): 77- 91.
6	Artzner P , Delbaen F , Eber J M , et al. Coherent measures of risk[J]. Mathematical Finance, 1999, 9 (3): 203- 228. doi: 10.1111/1467-9965.00068
7	Guo S , Xu H . Distributionally robust shortfall risk optimization model and its approximation[J]. Mathematical Programming, 2019, 174 (1/2): 473- 498.
8	Rockafellar R T , Uryasev S . Optimization of conditional value-at-risk[J]. Risk, 2000, 2 (3): 21- 41. doi: 10.21314/JOR.2000.038
9	刘强. 分布鲁棒优化的模型与稳定性研究[D]. 大连: 大连理工大学, 2018.
10	王炜, 包攀, 李三硕. 基于矩信息的不确定投资组合优化问题[J]. 辽宁师范大学学报(自然科学版), 2020, 43 (1): 1- 5.
11	Arrow K , Karlin S , Scarf H . Studies in the Mathematical Theory of Inventory and Production[M]. Stanford: Stanford University Press, 2005.
12	Shapiro A , Kleywegt A . Minimax analysis of stochastic problems[J]. Optimization Methods and Software, 2002, 17 (3): 523- 542. doi: 10.1080/1055678021000034008
13	Delage K , Ye Y . Distributionally robust optimization under moment uncertainty with application to data driven problems[J]. Operations Research, 2010, 58 (3): 592- 612.
14	Krokhmal P , Palmquist J , Uryasev S . Portfolio of optimization with conditional value-at-risk objective and constraints[J]. Risk, 2002, 4 (2): 11- 27.
15	Pshenichnyi B N . Necessary Conditions for an Extremum[M]. New York: Dekker, 1971.
16	Liu Y , Meskarian R , Xu H H . Distributionally robust reward-risk ratio optimization with moments constraints[J]. Optimization, 2017, 27 (2): 957- 985.
17	Xu H , Liu Y , Sun H . Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods[J]. Mathematical Programming, 2018, 169 (2): 489- 529. doi: 10.1007/s10107-017-1143-6
18	Mohajerin E P , Delage K . Data-draven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations[J]. Mathematical Programming, 2018, 171, 115- 166. doi: 10.1007/s10107-017-1172-1
19	Ahmed S , Cakmak U , Shapiro A . Coherent risk measures in inventory problems[J]. European Journal of Operational Research, 2006, 182 (1): 226- 238.
20	Su J. An analytical assessment of generation asset in the restructured electricity industry[D]. Hong Kong: University of Hong Kong, 2006.
21	Su J , Wu F F . Evaluation of generation expansion investment under competitive market environment[J]. IEEE Power Engineering Society General Meeting, 2005, 3, 2136- 2140.

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

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