Research on financial risk management methods based on new risk measures and their applications

在本研究项目中，我们取得了以下成果：(1)提出了用VaR度量风险的投资组合优化模型的有效求解方法。特别地，我们证明了VaR最小化模型可以通过求解一系列线性规划模型来求解，并提出了求解该模型的算法。(2)提出了用VaR度量市场风险的结构化产品的设计问题，并提出了相应的求解方法。(3)为了度量未来一段时间内的金融风险，我们提出并建立了期间风险价值的概念。为了建立基于PVaR的金融投资理论，我们开始探索计算PVaR和求解包含PVaR的投资组合优化模型的方法。

We got the following results in this research project (1)We proposed effective solution methods for solving portfolio optimization models with risk measured by VaR. Especially, we showed that VaR minimization model can be solved by solving a series of linear programming models, and proposed an algorithm for solving the model. (2)We formulated the design problem of structured products with market risk measured by VaR, and proposed methods for solving these models.(3)For measuring financial risk during a period of future time, we proposed and formulated the notion of Period Value at Risk(PVaR). To create a financial investment theory based on PVaR, we started to explore methods for computing PVaR and for solving portfolio optimization models with PVaR included.