• 论文 •

### 多周期多目标条件风险值模型

1. 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

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

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