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Preprint 03-2020

Model order reduction for parametric high dimensional models in the analysis of financial risk

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Author(s) : Andreas Binder, Onkar Jadhav , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 03-2020

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

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.

Keywords : 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 (PRIIPs)

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