Error analysis of a model order reduction framework for financial risk analysis

[摘要] A parametric model order reduction (MOR) approach for simulating high-dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model approximations for high-dimensional parametric convection-diffusion reaction partial differential equations (PDE). The proposed technique uses an adaptive greedy sampling approach based on surrogate modeling to efficiently locate the most relevant training parameters, thus generating the optimal reduced basis. The best suitable reduced model is procured such that the total error is less than a user-defined tolerance. The three major errors considered are the discretization error associated with the full model obtained by discretizing the PDE, the model order reduction error, and the parameter sampling error. The developed technique is analyzed, implemented, and tested on industrial data of a puttable steepener under the two-factor Hull-White model. The results illustrate that the reduced model provides a significant speedup with excellent accuracy over a full model approach, demonstrating its potential for applications to the historical or Monte Carlo Value-at-Risk calculations.

[学科分类] 数学（综合）

[关键词] financial risk analysis;short-rate models;convection-diffusion-reaction equation;finite element method;parametric model order reduction;proper orthogonal decomposition;adaptive greedy sampling;error analysis;packaged retail investment and insurance-based products