Much of financial theory neglects transactions costs. Perhaps the most successful implementation of it -- i.e. continuous-time portfolio choice and option pricing -- is downright inconsistent with the existence of any transactions cost at all. Nonetheless prima facie evidence from the trade is that transactions costs are a source of concern for portfolio managers. The presence of practically any friction in financial markets qualitatively changes the nature of the optimization problem; for it produces the need sometimes to do nothing and sometimes to act, an issue which, of course, does not arise in frictionless situations.
The investor considered here does not consume along the way. He accumulates wealth until some terminal point in time. At that point he consumes all. His objective is to maximize the expected utility derived from that terminal consumption. We postpone the terminal point infinitely far into the future to obtain a stationary portfolio rule. The optimal portfolio policy which we find is in the form of two control barriers between which portfolio proportions are allowed to fluctuate before some trade is resorted to.
We show how to calculate these two barriers exactly.
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