This paper presents a model order reduction approach for large scale high dimensional parametric models arising in the analysis of financial risk. To understand the risks associated with a financial product, one has to perform several thousand computationally demanding simulations of the model which require efficient algorithms. We establish a model reduction approach based on a variant of the proper orthogonal decomposition method to generate small model approximations for the high dimensional parametric convection-diffusion-reaction partial differential equations. This approach requires to solve the full model at some selected parameter values to generate a reduced basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set. The new technique is analyzed, implemented, and tested on industrial data of a floater with cap and floor under the Hull–White model. The results illustrate that the reduced model approach works well for short-rate models.

中文翻译：

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金融风险分析中参数利率模型模拟的模型降阶

本文针对金融风险分析中出现的大规模高维参数模型提出了一种模型降阶方法。要了解与金融产品相关的风险，必须对模型执行数千次计算要求高的模拟，这需要有效的算法。我们建立了一种基于适当正交分解方法的变体的模型简化方法，以生成高维参数对流-扩散-反应偏微分方程的小模型近似值。这种方法需要在某些选定的参数值下求解完整模型以生成简化的基础。我们提出了一种基于代理建模的自适应贪婪采样技术，用于选择样本参数集。新技术被分析，实施，并在 Hull-White 模型下对带帽和底板的浮子的工业数据进行了测试。结果表明，简化模型方法适用于短期模型。