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运筹学学报 ›› 2018, Vol. 22 ›› Issue (4): 45-56.doi: 10.15960/j.cnki.issn.1007-6093.2018.04.004

• 运筹学 • 上一篇    下一篇

多损失WCVaR模型的等价性定理

徐蕾艳1,2  孟志青1,*   

  1. 1. 浙江工业大学经贸管理学院, 杭州 310023;  2. 浙江财经大学, 杭州 310018
  • 收稿日期:2017-08-26 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 孟志青 E-mail: mengzhiqing@zjut.edu.cn
  • 基金资助:

    浙江省自然科学基金(No. LY15G010007)

General equivalence problem of multi-loss WCVaR

XU Leiyan1,2  MENG Zhiqing1,*   

  1. 1. College of Economics and Management, Zhejiang University of Technology, Hangzhou 320023, China; 2. Zhejiang University of Finance & Economics, Hangzhou 310018, China
  • Received:2017-08-26 Online:2018-12-15 Published:2018-12-15

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摘要：

研究了多概率分布簇下的多损失下的WCVaR(Multi Worst Conditional Value-at-Risk)模型等价性定理, 根据概率分布簇的VaR测度值, 定义了多损失下的WCVaR风险测度值和对应的多目标优化模型(MWCVaR), 证明了多目标优化模型(MWCVaR)等价另一个多目标优化模型求解. 对于有限分布簇情形, 在一定条件下, 证明了用有限个分布簇就可以近似计算多损失(MWCVaR)优化模型.

关键词: 多目标条件风险值, MWCVaR, 概率分布簇, 等价优化定理

Abstract:

Under multi-probability distribution cluster, equivalence of multi-loss WCVaR (Worst Conditional Value-at-Risk, MCVaR) problem is studied. According to the VaR measure under multi-probability distribution cluster, the multi-objective optimization problem (MWCVaR) is defined by the WCVaR risk measurement. It is proved that the optimization problem (MWCVaR) is equivalent to solve another multi-objective optimization problem. In the case of a finite distributions cluster, under certain conditions, we prove that the Pareto effective solution of the problem (MWCVaR) can be approximated by a finite distributions cluster.

Key words: multi-objective conditional value at risk, MWCVaR, probability distribution cluster, equivalent optimization theorem