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

摘要

We study a single risky financial asset model subject to price impact andtransaction cost over an infinite horizon. An investor needs to execute a longposition in the asset affecting the price of the asset and possibly incurringin fixed transaction cost. The objective is to maximize the discounted revenueobtained by this transaction. This problem is formulated first as an impulsecontrol problem and we characterize the value function using the viscositysolutions framework. We also analyze the case where there is no transactioncost and how this formulation relates with a singular control problem. Aviscosity solution characterization is provided in this case as well. We alsoestablish a connection between both formulations with zero fixed transactioncost. Numerical examples with different types of price impact conclude thediscussion.