金融市场中资产价格常常呈现出一定的“长相依性、尖峰厚尾”等特征及利率具有随机波动性，现有的资产价格模型不能准确刻画金融实际情况。本项目针对传统资产价格模型的不足，将构建混合高斯Heston资产价格模型，深入探讨混料试验设计在投资组合中的应用。研究主要包括以下三个方面：（1）资产价格模型研究。拟建立混合高斯Heston资产价格模型，对模型中的未知参数进行估计和敏感性分析；用随机分析方法推导美式期权满足的随机偏微分方程，获得数值解。（2)混料试验设计在投资组合中的应用研究。基于混料试验设计理论，构建随机误差项有异方差和自相关性的混料模型，推导混合准则下的最优投资组合方式；计算资产投资组合价值。（3）风险度量与管理研究。利用Monte Carlo模拟计算条件“在险价值”，提出金融风险管理对策。成果有助于深化了解美式期权定价过程，推动混料试验设计理论发展，为风险管理提供决策依据。

In the financial market, the asset price often presents some characteristics,such as "long dependence,sharp peak and thick tail" and the interest rate has stochastic volatility. The existing asset price model cannot accurately describe the financial reality. Aiming at the shortcomings of the traditional asset price model, a mixed Gaussian Heston asset price model will be bulit in the project, and the application of designs of mixture experiments will be discussed in portfolio. The research mainly includes the following three aspects :(1) Research on asset price model. The mixed Gaussian Heston asset price model will be built, to estimate and analyze the unknown parameters in the model. The stochastic partial differential equations satisfied by American options are derived by stochastic analysis, and the numerical solutions are obtained,respectivly. (2) Research on the application of designs of mixture experiments in portfolio. Based on the theory of designs of mixture experiments, a mixed material model with heteroscedasticity and autocorrelation for random error term is constructed, and the optimal portfolio mode under mixed criteria is deduced. (3) Research on risk measurement and management. The value of asset portfolio will be calculated, and Monte Carlo simulation will be used to calculate the conditional "Value at Risk", and financial risk management countermeasures will be proposed. The results are helpful to deepen the understanding of American options pricing processes, promote the development of theory of designs of mixture experiments, and provide decision-making basis for risk management.