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Asset liquidation under drift uncertainty and regime-switching volatility

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  • 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
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    References listed on IDEAS

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    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," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    3. 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.
    4. 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.
    5. 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..
    6. Erik Ekström & Johan Tysk, 2008. "Convexity theory for the term structure equation," Finance and Stochastics, Springer, vol. 12(1), pages 117-147, January.
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