Portfolio selection with transaction costs. (English) Zbl 0717.90007

Summary: 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 in the literature 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.


91G10 Portfolio theory
93E20 Optimal stochastic control
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91-08 Computational methods for problems pertaining to game theory, economics, and finance
91B62 Economic growth models
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