Optimal execution strategy in the presence of permanent price impact and fixed transaction cost

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.