IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v31y2023i3d10.1007_s11750-022-00652-2.html
   My bibliography  Save this article

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

Author

Listed:
  • Héctor Jasso-Fuentes

    (Department of Mathematics)

  • Carlos G. Pacheco

    (Department of Mathematics)

  • Gladys D. Salgado-Suárez

    (Department of Mathematics)

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.

Suggested Citation

  • Héctor Jasso-Fuentes & Carlos G. Pacheco & Gladys D. Salgado-Suárez, 2023. "A discrete-time optimal execution problem with market prices subject to random environments," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 562-583, October.
  • Handle: RePEc:spr:topjnl:v:31:y:2023:i:3:d:10.1007_s11750-022-00652-2
    DOI: 10.1007/s11750-022-00652-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-022-00652-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11750-022-00652-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Olivier Guéant & Jiang Pu, 2017. "Option Pricing And Hedging With Execution Costs And Market Impact," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 803-831, July.
    2. Isabel Castro & Carlos G. Pacheco, 2020. "Modeling and pricing with a random walk in random environment," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 1-20, December.
    3. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    4. Masaaki Fukasawa & Masamitsu Ohnishi & Makoto Shimoshimizu, 2021. "Discrete-Time Optimal Execution Under A Generalized Price Impact Model With Markovian Exogenous Orders," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-43, August.
    5. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    6. Julian Lorenz & Robert Almgren, 2011. "Mean--Variance Optimal Adaptive Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(5), pages 395-422, January.
    7. Christos H. Papadimitriou & John N. Tsitsiklis, 1987. "The Complexity of Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 441-450, August.
    8. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    9. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.
    10. Ghulam Sarwar, 2003. "The interrelation of price volatility and trading volume of currency options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(7), pages 681-700, July.
    11. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    12. Masamitsu Ohnishi & Makoto Shimoshimizu, 2020. "Optimal and equilibrium execution strategies with generalized price impact," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1625-1644, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Masamitsu Ohnishi & Makoto Shimoshimizu, 2024. "Trade execution games in a Markovian environment," Papers 2405.07184, arXiv.org.
    2. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    3. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    4. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    5. Zhao, Jingdong & Zhu, Hongliang & Li, Xindan, 2018. "Optimal execution with price impact under Cumulative Prospect Theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1228-1237.
    6. Siu, Chi Chung & Guo, Ivan & Zhu, Song-Ping & Elliott, Robert J., 2019. "Optimal execution with regime-switching market resilience," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 17-40.
    7. Yan, Tingjin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Portfolio liquidation with delayed information," Economic Modelling, Elsevier, vol. 126(C).
    8. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.
    9. Xiangge Luo & Alexander Schied, 2018. "Nash equilibrium for risk-averse investors in a market impact game with transient price impact," Papers 1807.03813, arXiv.org, revised Jun 2019.
    10. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    11. Jin Fang & Jiacheng Weng & Yi Xiang & Xinwen Zhang, 2022. "Imitate then Transcend: Multi-Agent Optimal Execution with Dual-Window Denoise PPO," Papers 2206.10736, arXiv.org.
    12. repec:dau:papers:123456789/7391 is not listed on IDEAS
    13. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    14. David Evangelista & Yuri Saporito & Yuri Thamsten, 2022. "Price formation in financial markets: a game-theoretic perspective," Papers 2202.11416, arXiv.org.
    15. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    16. David Evangelista & Yuri Thamsten, 2023. "Approximately optimal trade execution strategies under fast mean-reversion," Papers 2307.07024, arXiv.org, revised Aug 2023.
    17. Olivier Gu'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Dec 2014.
    18. Qixuan Luo & Shijia Song & Handong Li, 2023. "Research on the Effects of Liquidation Strategies in the Multi-asset Artificial Market," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1721-1750, December.
    19. Takashi Kato, 2011. "An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised Jul 2014.
    20. Gianbiagio Curato & Jim Gatheral & Fabrizio Lillo, 2014. "Optimal execution with nonlinear transient market impact," Papers 1412.4839, arXiv.org.
    21. Daniel Hern'andez-Hern'andez & Harold A. Moreno-Franco & Jos'e Luis P'erez, 2017. "Periodic strategies in optimal execution with multiplicative price impact," Papers 1705.00284, arXiv.org, revised May 2018.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:topjnl:v:31:y:2023:i:3:d:10.1007_s11750-022-00652-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.