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An Optimal Control Approach to Portfolio Optimisation with Conditioning Information

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  • Marc Boissaux

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

  • Jang Schiltz

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

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    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.

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    Bibliographic Info

    Paper provided by Luxembourg School of Finance, University of Luxembourg in its series LSF Research Working Paper Series with number 10-09.

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    Date of creation: 2010
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    Handle: RePEc:crf:wpaper:10-09

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    Keywords: Optimal Control; Portfolio Optimization;

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    References

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    1. Miroslav Misina, 2003. "What Does the Risk-Appetite Index Measure?," Working Papers 03-23, Bank of Canada.
    2. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
    3. repec:ebl:ecbull:v:28:y:2003:i:6:p:a6 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Miroslav Misina, 2006. "Benchmark Index of Risk Appetite," Working Papers 06-16, Bank of Canada.
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    Cited by:
    1. 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.
    2. Jang Schiltz & Marc Boissaux, 2013. "A Numerical Scheme for Multisignal Weight Constrained Conditioned Portfolio Optimisation Problems," CREA Discussion Paper Series 13-3, Center for Research in Economic Analysis, University of Luxembourg.

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