多周期多目标条件风险值模型

doi:10.12341/jssms10374

系统科学与数学 ›› 2011, Vol. 31 ›› Issue (4): 414-428.DOI: 10.12341/jssms10374

多周期多目标条件风险值模型

蒋敏, 孟志青

浙江工业大学经贸管理学院

收稿日期:2010-08-12 修回日期:1900-01-01 出版日期:2011-04-25 发布日期:2011-08-16

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蒋敏;孟志青. 多周期多目标条件风险值模型[J]. 系统科学与数学, 2011, 31(4): 414-428.

JIANG Min;MENG Zhiqing. MULTI-PERIODS MULTIOBJECTIVE CONDITIONAL VALUE-AT-RISK MODEL[J]. Journal of Systems Science and Mathematical Sciences, 2011, 31(4): 414-428.

MULTI-PERIODS MULTIOBJECTIVE CONDITIONAL VALUE-AT-RISK MODEL

JIANG Min, MENG Zhiqing

College of Business and Administration, Zhejiang University of Technology

Received:2010-08-12 Revised:1900-01-01 Online:2011-04-25 Published:2011-08-16

在商业、工业、电力和房地产等行业中存在许多复杂的多周期风险决策问题, 它的数学模型研究对于解决这些问题具有重要的作用. 作者建立了一种新的多周期多目标条件风险值(CVaR)数学模型理论和方法. 先定义了一种带时间段的多周期多目标损失函数下的$\alpha$-VaR和$\alpha$-CVaR值, 给出了一类多周期多目标CVaR最优化模型. 然后, 证明了多目标意义下的对应模型
的等价定理, 给出了多周期多目标 CVaR模型的近似求解等价模型. 最后, 建立了一种生产企业在供过于求和供不应求两种情形下产生的多周期双目标 CVaR模型, 针对一个电力生产企业进行的数值实验, 表明了模型可以得到在最小供给的用电损失分布下的各周期下的相匹配供电策略, 可以帮助供电部门各个时期供电不平衡状况下的风险控制.

关键词： 条件风险值, 多周期风险决策, 多目标CVaR模型, 损失函数.

There are many complex risk decision making problems in fields of business, industry, power and real estate. It is very useful to study the mathematical model of these problems for solving those problems. This paper proposes theory and method of a new multi-periods multiobjective conditional value-at-risk (CVaR) model. The concepts of the ${\bm \alpha}$-VaR and ${\bm \alpha}$-CVaR are introduced for the case of multiple losses under the confidence level vector ${\bm\alpha}$ with respective to multi-periods. A multiobjective CVaR problem with period is established to solve the minimal ${\bm \alpha}$-CVaR model. It is show that the CVaR problem with time is equal to another optimal problem based on weight. Therefore the CVaR problem can be transformed into an approximate linear program. Finally, a multi-periods two-objective CVaR model of production enterprise is established to find out the robust period and strategy. The numerical results indicate that the best period and strategy of supplying electricity can be given based on the above theory. By sensitivity analysis,
supplying electricity plan may be regulated with price and quantity
to evade loss of risk.

Key words: Conditional value-at-risk, multi-periods risk deicison making peoblems, mutliobjective CVaR model, loss function.

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