Portfolio Selection with Transaction Costs

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 costle...

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Bibliographic Details
Published in:Mathematics of operations research 1990-11, Vol.15 (4), p.676-713
Main Authors: Davis, M. H. A, Norman, A. R
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Bank assets
Bank stocks
Dynamic programming
Endowments
Exact sciences and technology
free boundary problem
Investment policy
Investors
local time
Mathematical analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Operations research
Optimal
Optimal policy
Portfolio investments
Portfolio selection
Portfolio theory
reflecting diffusions
stochastic control
Stock sales
Stock transactions
Theory
Trajectories
Transaction costs
Utility functions
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Summary: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.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.15.4.676