  We investigate the general structure of optimal investment and consumption
with small proportional transaction costs. For a safe asset and a risky asset
with general continuous dynamics, traded with random and time-varying but small
transaction costs, we derive simple formal asymptotics for the optimal policy
and welfare. These reveal the roles of the investors' preferences as well as
the market and cost dynamics, and also lead to a fully dynamic model for the
implied trading volume. In frictionless models that can be solved in closed
form, explicit formulas for the leading-order corrections due to small
transaction costs are obtained.
