  We study long-term growth-optimal strategies on a simple market with linear
proportional transaction costs. We show that several problems of this sort can
be solved in closed form, and explicit the non-analytic dependance of optimal
strategies and expected frictional losses of the friction parameter. We present
one derivation in terms of invariant measures of drift-diffusion processes
(Fokker- Planck approach), and one derivation using the Hamilton-Jacobi-Bellman
equation of optimal control theory. We also show that a significant part of the
results can be derived without computation by a kind of dimensional analysis.
We comment on the extension of the method to other sources of uncertainty, and
discuss what conclusions can be drawn about the growth-optimal criterion as
such.
