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

• Published in: TOP Vol. 31; no. 3; pp. 562 - 583
• Main Authors: Jasso-Fuentes, Héctor, Pacheco, Carlos G., Salgado-Suárez, Gladys D.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023; Springer Nature B.V
• Subjects: Business and Management; Dynamic programming; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Industrial and Production Engineering; Insurance; Management; Mathematical models; Operations Research/Decision Theory; Optimization; Original Paper; Statistics for Business; Random environment; 90C40; Random walks; 91G15; 82B41; 60K37; Price impacts; Dynamic programming; Optimal execution problems
• ISSN: 1134-5764; 1863-8279
• DOI: 10.1007/s11750-022-00652-2

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.