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

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Abstract

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.

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Funding

This research was funded in part by: Conacyt scholarship No. 1220142 “2do Año de continuidad de estancias posdoctorales por México 2021”, and by Grants: Conacyt Ciencia de Frontera No. 87787 and PRODEP-2021 No. CA-38.

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Authors and Affiliations

  1. Department of Mathematics, CINVESTAV-IPN, Mexico, Mexico

    Héctor Jasso-Fuentes, Carlos G. Pacheco & Gladys D. Salgado-Suárez

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  1. Héctor Jasso-Fuentes
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  2. Carlos G. Pacheco
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  3. Gladys D. Salgado-Suárez
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Correspondence to Héctor Jasso-Fuentes.

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Jasso-Fuentes, H., Pacheco, C.G. & Salgado-Suárez, G.D. A discrete-time optimal execution problem with market prices subject to random environments. TOP 31, 562–583 (2023). https://doi.org/10.1007/s11750-022-00652-2

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  • DOI: https://doi.org/10.1007/s11750-022-00652-2

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