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An Optimal Control Approach to Portfolio Optimisation with Conditioning Information

Author

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  • Marc Boissaux

    () (Luxembourg School of Finance, University of Luxembourg)

  • Jang Schiltz

    () (Luxembourg School of Finance, University of Luxembourg)

Abstract

In the classical discrete-time mean-variance context, a method for portfolio optimisation using conditioning information was introduced in 2001 by Ferson and Siegel ([1]). The fact that there are many possible signals that could be used as conditioning information, and a number of empirical studies that suggest measurable relationships between signals and returns, causes this type of portfolio optimisation to be of practical as well as theoretical interest. Ferson and Siegel obtain analytical formulae for the basic unconstrained portfolio optimisation problem. We show how the same problem, in the presence of a riskfree asset and given a single conditioning information time series, may be expressed as a general constrained infinite-horizon optimal control problem which encompasses the results in [1] as a special case. Variants of the problem not amenable to closed-form solutions can then be solved using standard numerical optimal control techniques. We extend the standard finite-horizon optimal control sufficiency and necessity results of the Pontryagin Maximum Principle and the Mangasarian sufficiency theorem to the doubly-infinite horizon case required to cover our formulation in its greatest generality. As an application, we rephrase the previously unsolved constrained-weight variant of the problem in [1] using the optimal control framework and derive the specific necessary conditions applicable. Finally, we carry out simulations involving numerical solution of the resulting optimal control problem to assess the extent to which the use of conditioning information brings about practical improvements in the field of portfolio optimisation.

Suggested Citation

  • 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.
  • Handle: RePEc:crf:wpaper:10-09
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    References listed on IDEAS

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    1. Prasanna Gai & Nicholas Vause, 2006. "Measuring Investors' Risk Appetite," International Journal of Central Banking, International Journal of Central Banking, vol. 2(1), March.
    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. Miroslav Misina, 2006. "Benchmark Index of Risk Appetite," Staff Working Papers 06-16, Bank of Canada.
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    5. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    6. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    7. repec:ebl:ecbull:v:28:y:2003:i:6:p:a6 is not listed on IDEAS
    8. Devraj Basu & Chi-Hsiou Hung & Roel Oomen & Alexander Stremme, 2006. "When to Pick the Losers: Do Sentiment Indicators Improve Dynamic Asset Allocation?," Working Papers wpn06-13, Warwick Business School, Finance Group.
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    Cited by:

    1. repec:luc:wpaper:13-3 is not listed on IDEAS
    2. 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.

    More about this item

    Keywords

    Optimal Control; Portfolio Optimization;

    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
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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