  Proportional transaction costs present difficult theoretical problems in
trading algorithm design, on account of their lack of analytical tractability.
The author derives a solution of DT-NT-DT form for an arbitrary model in which
the the traded asset has diffusive dynamics described by one or more stochastic
risk factors. The width of the NT zone is found to be, as expected,
proportional to the cube root of the transaction cost. It is also proportional
to the 2/3 power of the volatility of the target position, thereby causing a
faster trading strategy to be buffered more than a slower one. The displacement
of the middle of the buffer from the costfree position is found to be
proportional to the square of the width, and hence to the 2/3 power of the
transaction cost; the proportionality constant depends on the expected
short-term change in position.
