A discrete-time optimal execution problem with market prices subject to random environments

In this paper we study an optimal asset liquidation problem for a discrete-time stochastic dynamics, involving a variant of the binomial price model that incorporates both a random environment present in the market and permanent shocks. Our aim is to find an optimal plan for the sale of assets at certain appropriate times to obtain the highest possible expected reward. To achieve this goal, the financial problem is presented as an impulsive control model in discrete time, whose solution is based on the well-known dynamic programming method. Under this method we obtain: (1) the seller's optimal expected profit and (2) optimal sale strategies. In addition we mention how one can use the so-called potential function to analyze the influence of the environment on the trend of the prices and as a byproduct to infer how this trending influences the optimal sale strategies. We provide numerical simulations to illustrate our findings.