Portfolio management with transaction costs: an asymptotic analysis of the Morton and Pliska model. (English) Zbl 0866.90010
Summary: We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no-transaction-cost solution. Although the full problem is a free-boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.
MSC:
| 91G10 | Portfolio theory |
References:
| [1] | DOI: 10.1016/0165-1889(90)90004-Z · Zbl 0715.90017 · doi:10.1016/0165-1889(90)90004-Z |
| [2] | Eastham J. F., Math. Oper. Res. 13 pp 588– (1988) |
| [3] | DOI: 10.1016/0022-0531(71)90038-X · Zbl 1011.91502 · doi:10.1016/0022-0531(71)90038-X |
| [4] | A. J. Morton, and S. R. Pliska (1993 ): ”Optimal Portfolio Management with Fixed Transaction Costs,” working paper. · Zbl 0866.90020 |
| [5] | Nayfeh A. H., Introduction to Perturbation Techniques. (1981) · Zbl 0449.34001 |
| [6] | Dyke M., Perturbation methods in fluid mechanics (1975) · Zbl 0329.76002 |
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