Davis, M. H. A.; Norman, A. R. Portfolio selection with transaction costs. (English) Zbl 0717.90007 Math. Oper. Res. 15, No. 4, 676-713 (1990). 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. Cited in 5 ReviewsCited in 317 Documents 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 Keywords:optimal consumption and investment decisions; log-normal diffusion; optimal buying and selling policies PDFBibTeX XMLCite \textit{M. H. A. Davis} and \textit{A. R. Norman}, Math. Oper. Res. 15, No. 4, 676--713 (1990; Zbl 0717.90007) Full Text: DOI Link