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A Minimum Variance Result in Continuous Trading Portfolio Optimization

Author

Listed:
  • Henry R. Richardson

    (United States Naval Academy, Annapolis, Maryland 21401 and Center for Naval Analyses)

Abstract

The problem of minimizing the variance of discounted wealth at the end of a fixed period is solved when the expectation of terminal wealth is constrained to a specified investment goal. The results are obtained in a continuous trading framework under the assumption that the funds can be exchanged between a riskless bond and a stock whose discounted price is described by a geometric Brownian motion. Transaction costs are ignored (i.e., the market is "frictionless") and unlimited borrowing is permitted at the same rate as the return on the bond. Typically the optimal trading policy under the above assumptions involves a highly leveraged investment in the stock in the early stages followed by an accumulation of the bond in the later stages. Numerical results are provided as an illustration of the theory.

Suggested Citation

  • Henry R. Richardson, 1989. "A Minimum Variance Result in Continuous Trading Portfolio Optimization," Management Science, INFORMS, vol. 35(9), pages 1045-1055, September.
  • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:9:p:1045-1055
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    File URL: http://dx.doi.org/10.1287/mnsc.35.9.1045
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    Citations

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    Cited by:

    1. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    2. 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.
    3. Jan Kallsen & Johannes Muhle-Karbe, 2013. "The General Structure of Optimal Investment and Consumption with Small Transaction Costs," Papers 1303.3148, arXiv.org, revised May 2015.
    4. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    5. Chenghu Ma, 2013. "MPS Risk Aversion and MV Analysis in Continuous Time with Lévy Jumps," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Bekker, Paul A., 2004. "A mean-variance frontier in discrete and continuous time," CCSO Working Papers 200406, University of Groningen, CCSO Centre for Economic Research.
    7. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678, arXiv.org.
    8. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    9. He, Lin & Liang, Zongxia, 2013. "Optimal investment strategy for the DC plan with the return of premiums clauses in a mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 643-649.
    10. Chi Kin Lam & Yuhong Xu & Guosheng Yin, 2016. "Dynamic portfolio selection without risk-free assets," Papers 1602.04975, arXiv.org.
    11. repec:dgr:rugccs:200406 is not listed on IDEAS
    12. repec:eee:insuma:v:76:y:2017:i:c:p:172-184 is not listed on IDEAS
    13. Christoph Czichowsky, 2013. "Time-consistent mean-variance portfolio selection in discrete and continuous time," Finance and Stochastics, Springer, vol. 17(2), pages 227-271, April.
    14. Nguyen, Pascal & Portait, Roland, 2002. "Dynamic asset allocation with mean variance preferences and a solvency constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 11-32, January.

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