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Monte Carlo approximate tensor moment simulations
Author(s) -
Arismendi Juan Carlos,
Kimura Herbert
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2056
Subject(s) - cholesky decomposition , mathematics , tensor (intrinsic definition) , monte carlo method , residual , moment (physics) , minimum degree algorithm , mathematical optimization , matrix (chemical analysis) , algorithm , statistics , incomplete cholesky factorization , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , classical mechanics , pure mathematics , composite material
Summary An algorithm to generate samples with approximate first‐order, second‐order, third‐order, and fourth‐order moments is presented by extending the Cholesky matrix decomposition to a Cholesky tensor decomposition of an arbitrary order. The tensor decomposition of the first‐order, second‐order, third‐order, and fourth‐order objective moments generates a non‐linear system of equations. The algorithm solves these equations by numerical methods. The results show that the optimization algorithm delivers samples with an approximate residual error of less than 10 16 between the components of the objective and the sample moments. The algorithm is extended for a n ‐th‐order approximate tensor moment version, and simulations of non‐normal samples replicated from distributions with asymmetries and heavy tails are presented. An application for sensitivity analysis of portfolio risk assessment with Value‐at‐Risk ( VaR ) is provided. A comparison with previous methods available in the literature suggests that the methodology proposed reduces the error of the objective moments in the generated samples. Copyright © 2016 John Wiley & Sons, Ltd.