  We study a single risky financial asset model subject to price impact and
transaction cost over an infinite horizon. An investor needs to execute a long
position in the asset affecting the price of the asset and possibly incurring
in fixed transaction cost. The objective is to maximize the discounted revenue
obtained by this transaction. This problem is formulated first as an impulse
control problem and we characterize the value function using the viscosity
solutions framework. We also analyze the case where there is no transaction
cost and how this formulation relates with a singular control problem. A
viscosity solution characterization is provided in this case as well. We also
establish a connection between both formulations with zero fixed transaction
cost. Numerical examples with different types of price impact conclude the
discussion.
