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A Numerical Scheme for Multisignal Weight Constrained Conditioned Portfolio Optimisation Problems

Author

Listed:
  • Jang Schiltz
  • Marc Boissaux

    (LSF)

Abstract

In this paper, we consider optimal control problems involving a multidimensional objective function integral. We propose a direct collocation discretisation scheme suitable for the numerical solution of problems of this type. A convergence result is established to show that the scheme is consistent with multidimensional Pontryagin Principle relations in several important respects. Whilst the discussion focuses on the two-dimensional case, the simplicity of the scheme allows for easy generalisation. As an application taken from the domain of finance, we then introduce conditioned portfolio optimisation. The optimal control transcription of the two-dimensional mean-variance problem is given and solved using the scheme under consideration. We carry out a backtest using real-world data and confirm that its results validate our proposed numerical scheme.

Suggested Citation

  • Jang Schiltz & Marc Boissaux, 2013. "A Numerical Scheme for Multisignal Weight Constrained Conditioned Portfolio Optimisation Problems," LSF Research Working Paper Series 13-3, Luxembourg School of Finance, University of Luxembourg.
    • Handle: RePEc:crf:wpaper:13-3
    as

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    File URL: http://wwwen.uni.lu/content/download/61990/723764/file/Binder3_A%20Numerical%20Scheme%20for%20Multisignal%20Weight%20Constrained_03.2013.pdf
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    2. Coudert, Virginie & Gex, Mathieu, 2008. "Does risk aversion drive financial crises? Testing the predictive power of empirical indicators," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 167-184, March.
    3. Marc Boissaux & Jang Schiltz, 2010. "An Optimal Control Approach to Portfolio Optimisation with Conditioning Information," LSF Research Working Paper Series 10-09, Luxembourg School of Finance, University of Luxembourg.
    4. V. Coudert & M. Gex, 2008. "Does risk aversion drive financial crises? Testing the predictive power of empirical indicators," Post-Print halshs-00321667, HAL.
    5. Wayne E. Ferson & Andrew F. Siegel, 2001. "The Efficient Use of Conditioning Information in Portfolios," Journal of Finance, American Finance Association, vol. 56(3), pages 967-982, June.
    6. Jang Schiltz & Marc Boissaux, 2011. "Practical weight-constrained conditioned portfolio optimization using risk aversion indicator signals," LSF Research Working Paper Series 11-12, Luxembourg School of Finance, University of Luxembourg.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Optimal Control; Direct Collocation; Multidimensional Problem;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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