论文标题
分析财务风险的参数高维模型的模型订单降低
Model order reduction for parametric high dimensional models in the analysis of financial risk
论文作者
论文摘要
本文在分析财务风险中提出了一种模型订单减少（MOR）方法，以实现高维问题。要了解财务风险和可能的结果，我们必须对基础产品进行数千次模拟。这些模拟很昂贵，并需要有效的计算性能。因此，为解决这个问题，我们基于适当的正交分解（POD）方法建立了MOR方法。该研究涉及高维参数对流 - 扩散反应偏微分方程（PDE）的计算。 POD需要以某些参数值求解高维模型以生成降顺序。我们提出了一种基于替代建模的自适应贪婪抽样技术，用于选择对工业数据进行分析，实施和测试的样本参数集的选择。在船体白色模型下带有盖和地板的浮子的数值示例获得的结果表明，MOR方法适合短速率模型。
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the underlying product. These simulations are expensive and create a need for efficient computational performance. Thus, to tackle this problem, we establish a MOR approach based on a proper orthogonal decomposition (POD) method. The study involves the computations of high dimensional parametric convection-diffusion reaction partial differential equations (PDEs). POD requires to solve the high dimensional model at some parameter values to generate a reduced-order basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set that is analyzed, implemented, and tested on the industrial data. The results obtained for the numerical example of a floater with cap and floor under the Hull-White model indicate that the MOR approach works well for short-rate models.
