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Mean–variance efficiency with extended CIR interest rates

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  • René Ferland
  • François Watier

Abstract

We study a mean–variance investment problem in a continuous‐time framework where the interest rates follow Cox–Ingersoll–Ross dynamics. We construct a mean–variance efficient portfolio through the solutions of backward stochastic differential equations. We also give sufficient conditions under which an explicit analytic expression is available for the mean–variance optimal wealth of the investor. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • René Ferland & François Watier, 2010. "Mean–variance efficiency with extended CIR interest rates," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(1), pages 71-84, January.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:1:p:71-84
    DOI: 10.1002/asmb.767
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
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    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Isabelle Bajeux-Besnainou & Roland Portait, 1998. "Dynamic Asset Allocation in a Mean-Variance Framework," Management Science, INFORMS, vol. 44(11-Part-2), pages 79-95, November.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    9. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    10. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
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