An aspect of optimal regression design for LSMC

Weiß, Christian; Nikolić, Zoran

doi:10.1515/mcma-2019-2049

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…McLean (2014) justifies that from the perspective of numerical stability performing a QR decomposition on a monomial design matrix Z is asymptotically equivalent to using a Legendre design matrix Z and transforming the resulting coefficient estimator into the monomial one. Under the assumption of an orthonormal basis, Weiß and Nikolić (2019) have derived an explicit upper bound for the condition number of non-diagonal matrix 1 N (Z ) T (Z ) for N < ∞, where the factor 1 N is used for technical reasons. This upper bound increases in (1) the number of basis functions, (2) the Hardy-Krause variation of the basis, (3) the convergence constant of the low-discrepancy sequence, and (4) the outer scenario dimension.…”

Section: Numerical Stabilitymentioning

confidence: 99%

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Krah

Nikolić

Korn

2020

Risks

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Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the least-squares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over generalized linear model (GLM) and generalized additive model (GAM) methods to multivariate adaptive regression splines (MARS) and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.

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Section: Numerical Stabilitymentioning

confidence: 99%

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Krah

Nikolić

Korn

2020

Risks

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“…in computational finance (see e.g. [CMO97], [GW09], [Gla03], [Pas94], [WN19]). Therefore, it is of interest to know sharp bounds for the smallest achievable star-discrepancy…”

Section: Discrepancymentioning

confidence: 99%

A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy

Gnewuch,

Pasing,

Weiß

2020

Preprint

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We prove a generalized Faulhaber inequality to bound the sums of the j-th powers of the first n (possibly shifted) natural numbers. With the help of this inequality we are able to improve the known bounds for bracketing numbers of d-dimensional axis-parallel boxes anchored in 0 (or, put differently, of lower left orthants intersected with the d-dimensional unit cube [0, 1] d ). We use these improved bracketing numbers to establish new bounds for the star-discrepancy of negatively dependent random point sets and its expectation. We apply our findings also to the weighted star-discrepancy.

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“…McLean (2014) justifies that from the perspective of numerical stability performing a QR decomposition on a monomial design matrix Z is asymptotically equivalent to using a Legendre design matrix Z and transforming the resulting coefficient estimator into the monomial one. Under the assumption of an orthonormal basis, Weiß & Nikolić (2018) have derived an explicit upper bound for the condition number of non-diagonal matrix 1 N (Z ) T (Z ) for N < ∞, where the factor 1 N is used for technical reasons. This upper bound increases in (1) the number of basis functions, (2) the Hardy-Krause variation of the basis, (3) the convergence constant of the low-discrepancy sequence, and (4) the outer scenario dimension.…”

Section: Numerical Stabilitymentioning

confidence: 99%

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Krah¹,

Nikolić²,

Korn³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have to rely on suitable approximation techniques such as the leastsquares Monte Carlo (LSMC) method. The key idea of LSMC is to run only a few wisely selected simulations and to process their output further to obtain a risk-dependent proxy function of the loss. In this paper, we present and analyze various adaptive machine learning approaches that can take over the proxy modeling task. The studied approaches range from ordinary and generalized least-squares regression variants over GLM and GAM methods to MARS and kernel regression routines. We justify the combinability of their regression ingredients in a theoretical discourse. Further, we illustrate the approaches in slightly disguised real-world experiments and perform comprehensive out-of-sample tests.

show abstract

An aspect of optimal regression design for LSMC

Cited by 6 publications

References 15 publications

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy

Machine Learning in Least-Squares Monte Carlo Proxy Modeling of Life Insurance Companies

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