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Monte Carlo Approximate Tensor Moment Simulations

Author

Listed:
  • Juan C. Arismendi

    (ICMA Centre, Henley Business School, University of Reading)

  • Herbert Kimura

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

Suggested Citation

  • Juan C. Arismendi & Herbert Kimura, 2014. "Monte Carlo Approximate Tensor Moment Simulations," ICMA Centre Discussion Papers in Finance icma-dp2014-08, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2014-08
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    Citations

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    Cited by:

    1. Domino, Krzysztof, 2020. "Multivariate cumulants in outlier detection for financial data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    2. Krzysztof Domino, 2016. "The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios," Papers 1605.09181, arXiv.org, revised Aug 2016.
    3. Domino, Krzysztof, 2017. "The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 267-276.

    More about this item

    Keywords

    Monte Carlo Simulation; Higher-order Moments; Exact Moments Simulation; Stress-testing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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