基于权值的双层多损失条件风险值模型

BILEVEL MULTI-LOSS CONDITIONAL VALUE-AT-RISK MODEL BASED ON THE WEIGHTS

条件风险值模型是风险管理中的一种重要工具.文章研究了一种具有上下层决策的多损失条件风险值模型,引入了基于权值的多个损失函数下的α-VaR损失值(最小风险值)和α-CVaR损失值(最小风险值对应的条件期望损失值或条件风险价值度量)概念,提出了基于权值的双层多损失条件风险值模型,该模型的目标是求上下层的基于权值的多损失α-CVaR达最小的最优解,并证明了它可以通过另一个较容易求解的双层规划模型获得最优解.最后,给出含一个制造商与零售商的供应链关于一种产品的定价与订购的双层条件风险值模型,该模型可以求出供过于求和供不应求风险最小下的制造商最小批发价和零售商最优订购量.

The conditional value-at-risk model is an important tool in risk man- agement. This paper studies a multi-loss conditional value-at-risk model with upper and lower decision-making. We introduce the concept of α-VaR loss value （minimum value at risk） and α-CVaR loss value （minimum risk value corresponding to the loss of value of the conditional expectation or conditional value at risk measure） of a multi-loss function based on the weights. We propose a bilevel multi-loss conditional value-at-risk model based on the weights. The objective is to find out an optimal solution to the model of upper level and lower level value of multi-loss α-the CVaR＇s based on the weights. We show that it can be solved more easily through another bilevel programming model to obtain the optimal solution. Finally, we give a bilevel conditionM value-at-risk model, including pricing and ordering of a supply chain to manufacturers and retailers on a product model calculated the minimum wholesale price of oversupply and shortage of risk minimization under the manufacturer and retailers excellent order amount.