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Optimum Constrained Portfolio Rules in a Diffusion Market

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  • Fernando Durrell

Abstract

A portfolio selection model is derived for diffusions where inequality constraints are imposed on portfolio security weights. Using the method of stochastic dynamic programming Hamilton-Jacobi-Bellman (HJB) equations are obtained for the problem of maximizing the expected utility of terminal wealth over a finite time horizon. Optimal portfolio weights are given in feedback form in terms of the solution of the HJB equations and its partial derivatives. An analysis of the no-constraining (NC) region of a portfolio is also conducted.

Suggested Citation

  • Fernando Durrell, 2006. "Optimum Constrained Portfolio Rules in a Diffusion Market," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 285-307.
    • Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:285-307
    DOI: 10.1080/13504860600840061
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    References listed on IDEAS

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    1. Vila, Jean-Luc & Zariphopoulou, Thaleia, 1997. "Optimal Consumption and Portfolio Choice with Borrowing Constraints," Journal of Economic Theory, Elsevier, vol. 77(2), pages 402-431, December.
    2. Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
    3. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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