• price impact;
  • impulse control;
  • singular control;
  • dynamic programming;
  • viscosity solutions


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 a 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 the value function is characterized 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. Copyright © 2011 John Wiley & Sons, Ltd.