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**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 |