An Optimal Control Approach to Portfolio Optimisation with Conditioning Information
In the classical discrete-time mean-variance context, a method for portfolio optimisation using conditioning information was introduced in 2001 by Ferson and Siegel (). 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  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  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.
|Date of creation:||2010|
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- Prasanna Gai & Nicholas Vause, 2006.
"Measuring Investors' Risk Appetite,"
International Journal of Central Banking,
International Journal of Central Banking, vol. 2(1), March.
- Prasanna Gai & Nicholas Vause, 2005. "Measuring investors' risk appetite," Bank of England working papers 283, Bank of England.
- Gai, Prasanna & Vause, Nicholas, 2005. "Measuring Investors' Risk Appetite," MPRA Paper 818, University Library of Munich, Germany.
- Miroslav Misina, 2003. "What does the risk-appetite index measure?," Economics Bulletin, AccessEcon, vol. 28(6), pages 1-6.
- Miroslav Misina, 2003. "What Does the Risk-Appetite Index Measure?," Staff Working Papers 03-23, Bank of Canada.
- 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.
- Virginie Coudert & Mathieu Gex, 2007. "Does Risk Aversion Drive Financial Crises? Testing the Predictive Power of Empirical Indicators," Working Papers 2007-02, CEPII research center.
- V. Coudert & M. Gex, 2008. "Does risk aversion drive financial crises? Testing the predictive power of empirical indicators," Post-Print halshs-00321667, HAL.
- repec:ebl:ecbull:v:28:y:2003:i:6:p:a6 is not listed on IDEAS
- Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
- Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
- 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.
- Miroslav Misina, 2006. "Benchmark Index of Risk Appetite," Staff Working Papers 06-16, Bank of Canada.
- 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. Full references (including those not matched with items on IDEAS)
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