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Monte Carlo Approximate Tensor Moment Simulations

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

Published on 29th September 2014
Authors Juan C. Arismendi, ICMA Centre, University of Reading and University of Brasilia and Herbert Kimura, University of Brasilia
Series Reference 2014-8
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