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Optimal Liquidation under Partial Information with Price Impact

Author

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  • Katia Colaneri
  • Zehra Eksi
  • Rudiger Frey
  • Michaela Szolgyenyi

Abstract

We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis. We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.

Suggested Citation

  • Katia Colaneri & Zehra Eksi & Rudiger Frey & Michaela Szolgyenyi, 2016. "Optimal Liquidation under Partial Information with Price Impact," Papers 1606.05079, arXiv.org, revised Jun 2019.
  • Handle: RePEc:arx:papers:1606.05079
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    References listed on IDEAS

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    1. 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.
    2. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 407-431.
    3. Nicole Bäuerle & Ulrich Rieder, 2009. "MDP algorithms for portfolio optimization problems in pure jump markets," Finance and Stochastics, Springer, vol. 13(4), pages 591-611, September.
    4. Claudia Ceci & Anna Gerardi, 2006. "A Model For High Frequency Data Under Partial Information: A Filtering Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 555-576.
    5. Nicole Bäuerle & Ulrich Rieder, 2007. "Portfolio Optimization With Jumps And Unobservable Intensity Process," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 205-224, April.
    6. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    7. Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
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    Cited by:

    1. David Evangelista & Yuri Thamsten, 2020. "On finite population games of optimal trading," Papers 2004.00790, arXiv.org, revised Feb 2021.
    2. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    3. Peter Kritzer & Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2017. "Approximation methods for piecewise deterministic Markov processes and their costs," Papers 1712.09201, arXiv.org, revised Jan 2019.

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