IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1701.08579.html
   My bibliography  Save this paper

Asset liquidation under drift uncertainty and regime-switching volatility

Author

Listed:
  • Juozas Vaicenavicius

Abstract

Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is modelled by $m$-state Markov chain. Using filtering theory, an equivalent reformulation of the original problem as a four-dimensional optimal stopping problem is found and then analysed by constructing approximating sequences of three-dimensional optimal stopping problems. An optimal liquidation strategy and various structural properties of the problem are determined. Analysis of the two-point prior case is presented in detail, building on which, an outline of the extension to the general prior case is given.

Suggested Citation

  • Juozas Vaicenavicius, 2017. "Asset liquidation under drift uncertainty and regime-switching volatility," Papers 1701.08579, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1701.08579
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1701.08579
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bing Lu, 2013. "Optimal Selling of an Asset with Jumps Under Incomplete Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(6), pages 599-610, December.
    2. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 14, pages 327-347, World Scientific Publishing Co. Pte. Ltd..
    3. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    4. G. Yin & Q. Zhang & F. Liu & R. H. Liu & Y. Cheng, 2006. "Stock Liquidation Via Stochastic Approximation Using Nasdaq Daily And Intra‐Day Data," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 217-236, January.
    5. Erhan Bayraktar, 2007. "A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions," Papers math/0703782, arXiv.org, revised Dec 2008.
    6. Erik Ekström & Johan Tysk, 2008. "Convexity theory for the term structure equation," Finance and Stochastics, Springer, vol. 12(1), pages 117-147, January.
    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. Erik Ekstrom & Juozas Vaicenavicius, 2015. "Optimal liquidation of an asset under drift uncertainty," Papers 1509.00686, arXiv.org.
    2. Erik Ekström & Martin Vannestål, 2019. "American Options And Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-14, September.
    3. Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    4. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    5. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    6. Alessandro Milazzo, 2024. "On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 336-358, October.
    7. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    8. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.
    9. Erhan Bayraktar & Hao Xing, 2009. "Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 505-525, December.
    10. Cheng-Feng Cheng, 2012. "Evaluate the Effectiveness of Manager Compensation," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 11(1), pages 25-44, June.
    11. Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2017. "Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization," European Journal of Operational Research, Elsevier, vol. 262(3), pages 851-862.
    12. Erhan Bayraktar & Zhou Zhou, 2012. "On controller-stopper problems with jumps and their applications to indifference pricing of American options," Papers 1212.4894, arXiv.org, revised Nov 2013.
    13. 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.
    14. Zsolt Nika & Mikl'os R'asonyi, 2019. "Learning Threshold-Type Investment Strategies with Stochastic Gradient Method," Papers 1907.02457, arXiv.org.
    15. G. Yin & Q. Zhang & C. Zhuang, 2010. "Recursive Algorithms for Trailing Stop: Stochastic Approximation Approach," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 209-231, July.
    16. 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.

    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:1701.08579. 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.