Arismendi Zambrano, Juan and Kimura, Herbert (2016) Monte Carlo Approximate Tensor Moment Simulations. Numerical Linear Algebra with Applications, 23 (5). pp. 825-847. ISSN 1099-1506

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Abstract

An algorithm to generate samples with approximate first-, second-, and third-order moments is presented extending the Cholesky matrix decomposition to a Cholesky tensor decomposition of an arbitrary order. The tensor decomposition of the first-, second-, and third-order objective moments generates a non-linear system of equations. The algorithm solves these equations by numerical methods. The results show that the optimisation algorithm delivers samples with an approximate error of 0.1%-4% between the components of the objective and the sample moments. 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 methodology proposed reduces the error of the objective moments in the generated samples.

Item Type:	Article
Additional Information:	This is the preprint version of the published article, which is available at: Arismendi, J. C., and Kimura, H. (2016) Monte Carlo approximate tensor moment simulations. Numer. Linear Algebra Appl., 23: 825–847. doi: 10.1002/nla.2056.
Keywords:	Monte Carlo Simulation; Higher-order Moments; Exact Moments Simulation; Stress-testing;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Social Sciences > Economics, Finance and Accounting
Item ID:	10201
Identification Number:	https://doi.org/10.1002/nla.2056
Depositing User:	Juan Arismendi Zambrano
Date Deposited:	09 Nov 2018 17:25
Journal or Publication Title:	Numerical Linear Algebra with Applications
Publisher:	Wiley
Refereed:	Yes
URI:	https://onlinelibrary.wiley.com/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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