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运筹学学报 >

2018 , Vol. 22 >Issue 4: 45 - 56

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2018.04.004

运筹学

多损失WCVaR模型的等价性定理

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  • 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

  网络出版日期: 2018-12-15

基金资助

浙江省自然科学基金(No. LY15G010007)

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General equivalence problem of multi-loss WCVaR

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  • 1. College of Economics and Management, Zhejiang University of Technology, Hangzhou 320023, China; 2. Zhejiang University of Finance & Economics, Hangzhou 310018, China

Received date: 2017-08-26

  Online 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

本文引用格式

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 . DOI: 10.15960/j.cnki.issn.1007-6093.2018.04.004

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

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