PORTFOLIO MANAGEMENT WITH TRANSACTION COSTS: AN ASYMPTOTIC ANALYSIS OF THE MORTON AND PLISKA MODEL

C. Atkinson and P. Wilmott

Mathematical Finance, 1995, vol. 5, issue 4, 357-367

Abstract: 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.

Date: 1995
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