风险的测度研究-对偶方法

面对开放的金融市场环境,金融风险的测度与防范已成为金融数学的研究热点之一.在考虑一个带有股票和债券的金融市场后,建立了具随机波动率的股票价格的随机微分方程模型.在这模型框架下,给出加权最小平均损失来测度风险的标准,于是问题转化为风险控制问题在此基础上,证明了最优风险控制策略的存在性并用对偶方法刻画了最优控制律的特征.

Study on risk measures-duality method

In the financial market system, the measures and hedging of financial risk are important. Considering a financial market with risky stocks and riskless bond, we describe the stochastic model of stocks prices with stochastic volatility. In the context of our model, we propose measuring risk as the smallest expected weighted loss. Thus, our problem is transformed into one of risk control. On the basis of this, the existence of optimal risk control strategy is proved. By duality approach, we characterize the optimal control law.