Error Analysis of a Model Order Reduction Framework for Financial Risk Analysis

@article{Binder2022ErrorAO,
  title={Error Analysis of a Model Order Reduction Framework for Financial Risk Analysis},
  author={Andreas Binder and Onkar Jadhav and Volker Mehrmann},
  journal={ArXiv},
  year={2022},
  volume={abs/2110.00774}
}
. 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… 

References

SHOWING 1-10 OF 64 REFERENCES
Model order reduction for the simulation of parametric interest rate models in financial risk analysis
TLDR
This paper establishes 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.
Variance-based sensitivity analysis of model outputs using surrogate models
A workout in computational finance
TLDR
Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.
Review of Discretization Error Estimators in Scientific Computing
TLDR
The goal of this paper is to review the different approaches for estimating discretization error and to present a general framework for their classification, and to address issues related to mesh refinement.
An adaptive step size controller for iterative implicit methods
On the generation of exact solutions for evaluating numerical schemes and estimating discretization error
Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media
TLDR
An adaptive time stepping strategy based on the estimation of the local truncation error via the Richardson extrapolation technique is described, which represents an interesting alternative to a fixed time step as shown by the various numerical tests involving reactive transport and unsaturated flow.
A New Look at Proper Orthogonal Decomposition
TLDR
Some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems are investigated and why in some applications this sensitivity is a concern while in others it is not.
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