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Portfolio Selection with Transaction Costs


  • M. H. A. Davis

    (Department of Electrical Engineering, Imperial College, London SW7 2BT, United Kingdom)

  • A. R. Norman

    (County Natwest, London, United Kingdom)


In this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account paying a fixed rate of interest and a stock whose price is a log-normal diffusion. This problem was solved by Merton and others when transactions between bank and stock are costless. Here we suppose that there are charges on all transactions equal to a fixed percentage of the amount transacted. It is shown that the optimal buying and selling policies are the local times of the two-dimensional process of bank and stock holdings at the boundaries of a wedge-shaped region which is determined by the solution of a nonlinear free boundary problem. An algorithm for solving the free boundary problem is given.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormoor:v:15:y:1990:i:4:p:676-713
    DOI: 10.1287/moor.15.4.676

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