IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1212.3145.html
   My bibliography  Save this paper

Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact

Author

Listed:
  • Baojun Bian
  • Nan Wu
  • Harry Zheng

Abstract

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime switching framework. The problem can be solved with the dynamic programming principle. The optimal value function is the unique continuous viscosity solution to the HJB equation and can be computed with the finite difference method.

Suggested Citation

  • Baojun Bian & Nan Wu & Harry Zheng, 2012. "Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact," Papers 1212.3145, arXiv.org, revised Oct 2014.
    • Handle: RePEc:arx:papers:1212.3145
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1212.3145
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    2. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    3. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    4. Moustapha Pemy & Qing Zhang & G. George Yin, 2008. "Liquidation Of A Large Block Of Stock With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 629-648, October.
    5. Paul Gassiat & Fausto Gozzi & Huyen Pham, 2011. "Investment/consumption problem in illiquid markets with regimes switching," Working Papers hal-00610214, HAL.
    6. repec:dau:papers:123456789/5599 is not listed on IDEAS
    7. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    8. Pemy, M. & Zhang, Q. & Yin, G., 2007. "Liquidation of a large block of stock," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1295-1305, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dmitry B. Rokhlin & Georgii Mironenko, 2016. "Regular finite fuel stochastic control problems with exit time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 105-127, August.

    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. Olivier Guéant & Jiang Pu, 2015. "Option pricing and hedging with execution costs and market impact," Post-Print hal-01393124, HAL.
    2. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    3. Lepinette, Emmanuel & Tran, Tuan, 2017. "Arbitrage theory for non convex financial market models," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3331-3353.
    4. Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
    5. Soner, H. Mete & Cetin, Umut & Touzi, Nizar, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
    6. Joaquin Fernandez-Tapia & Olivier Gu'eant, 2020. "Recipes for hedging exotics with illiquid vanillas," Papers 2005.10064, arXiv.org, revised May 2020.
    7. Olivier Gu'eant & Jiang Pu, 2013. "Option pricing and hedging with execution costs and market impact," Papers 1311.4342, arXiv.org, revised Apr 2015.
    8. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany.
    9. Villena, Marcelo J. & Reus, Lorenzo, 2016. "On the strategic behavior of large investors: A mean-variance portfolio approach," European Journal of Operational Research, Elsevier, vol. 254(2), pages 679-688.
    10. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    11. Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    12. Robert Jarrow, 2018. "Asset market equilibrium with liquidity risk," Annals of Finance, Springer, vol. 14(2), pages 253-288, May.
    13. Dolinsky, Yan & Zouari, Jonathan, 2021. "The value of insider information for super-replication with quadratic transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 394-416.
    14. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    15. Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    16. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    17. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
    18. Yan Dolinsky & Jonathan Zouari, 2019. "The Value of Insider Information for Super--Replication with Quadratic Transaction Costs," Papers 1910.09855, arXiv.org, revised Sep 2020.
    19. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. I: single-period case," Papers 1110.3224, arXiv.org, revised Dec 2013.
    20. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1212.3145. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.