UC Berkeley

We study a single risky financial asset model subject to price impact and transaction cost over infinite and finite 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 establish an associated optimal stopping problem that provides bounds and in some cases the solution of the value function. 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. An explicit solution of the value function is calculated in a particular case. Numerical examples with different types of price impact conclude the discussion.