多损失WCVaR模型的等价性定理  

General equivalence problem of multi-loss WCVaR

作　　者：徐蕾艳[1,2] 孟志青 XU Leiyan;MENG Zhiqing(College of Economics and Management,Zhejiang University of Technology,Hangzhou 320023,China;Zhejiang University of Financed Economics,Hangzhou 310018,China)

机构地区：[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

出　　处：《运筹学学报》2018年第4期45-56,共12页Operations Research Transactions

基　　金：浙江省自然科学基金(No.LY15G010007)

摘　　要：研究了多概率分布簇下的多损失下的WCVaR (Multi Worst Conditional Valueat-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.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.

关 键 词：多目标条件风险值 MWCVaR 概率分布簇 等价优化定理 

分 类 号：O122.2[理学—数学]