×

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.

MSC:

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
PDF BibTeX XML Cite
Full Text: DOI Link