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Main Title: Model order reduction for parametric high dimensional models in the analysis of financial risk
Author(s): Binder, Andreas
Jadhav, Onkar
Mehrmann, Volker
Type: Research Paper
Abstract: 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.
Subject(s): financial risk analysis
short-rate models
convection-diffusion reaction equation
finite difference method
parametric model order reduction
proper orthogonal decomposition
adaptive greedy sampling
packaged retail investment and insurance-based products
Issue Date: 27-Feb-2020
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 35L70 Nonlinear second-order PDE of hyperbolic type
65M06 Finite difference methods
62P05 Applications to actuarial sciences and financial mathematics
91-08 Computational methods
Sponsor/Funder: EC/H2020/765374/EU/Reduced Order Modelling, Simulation and Optimization of Coupled Systems/ROMSOC
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2020, 03
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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