| 多损失WCVaR模型的等价性定理 |
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| 引用本文： | 徐蕾艳,孟志青.多损失WCVaR模型的等价性定理[J].运筹学学报,2018,22(4):45-56. |
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| 作者姓名： | 徐蕾艳 孟志青 |
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| 作者单位： | 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 |
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| 基金项目： | 浙江省自然科学基金(No. LY15G010007) |
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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.
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| 关 键 词： | 多目标条件风险值 MWCVaR 概率分布簇 等价优化定理 |
| 收稿时间： | 2017-08-26 |
General equivalence problem of multi-loss WCVaR |
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| XU Leiyan,MENG Zhiqing.General equivalence problem of multi-loss WCVaR[J].OR Transactions,2018,22(4):45-56. |
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| Authors: | XU Leiyan MENG Zhiqing |
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| Institution: | 1. College of Economics and Management, Zhejiang University of Technology, Hangzhou 320023, China;
2. Zhejiang University of Finance & Economics, Hangzhou 310018, China |
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| 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. |
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| Keywords: | multi-objective conditional value at risk MWCVaR probability distribution cluster equivalent optimization theorem |
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