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Optimal portfolio liquidation in target zone models and catalytic superprocesses

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Listed:
  • Eyal Neuman

    (Hong Kong University of Science and Technology)

  • Alexander Schied

    (University of Mannheim)

Abstract

We study optimal buying and selling strategies in target zone models. In these models, the price is modelled by a diffusion process which is reflected at one or more barriers. Such models arise, for example, when a currency exchange rate is kept above a certain threshold due to central bank interventions. We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem is formulated as the minimization of a cost–risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting, the catalyst is given by the barriers of the price process. For the cases in which the unaffected price process is a reflected arithmetic or geometric Brownian motion with drift, we moreover give a detailed financial justification of our cost functional by means of an approximation with discrete-time models.

Suggested Citation

  • Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:2:d:10.1007_s00780-015-0280-0
    DOI: 10.1007/s00780-015-0280-0
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    References listed on IDEAS

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    1. Dawson, Donald A. & Fleischmann, Klaus, 1994. "A super-Brownian motion with a single point catalyst," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 3-40, January.
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    10. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
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    Citations

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    Cited by:

    1. Eyal Neuman & Alexander Schied, 2018. "Protecting Pegged Currency Markets from Speculative Investors," Papers 1801.07784, arXiv.org, revised Feb 2021.
    2. Eyal Neuman & Alexander Schied, 2022. "Protecting pegged currency markets from speculative investors," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 405-420, January.
    3. Dean Buckner & Kevin Dowd & Hardy Hulley, 2022. "Arbitrage Problems with Reflected Geometric Brownian Motion," Papers 2201.05312, arXiv.org, revised Sep 2022.
    4. Christoph Belak & Johannes Muhle-Karbe & Kevin Ou, 2018. "Optimal Trading with General Signals and Liquidation in Target Zone Models," Papers 1808.00515, arXiv.org.
    5. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    6. Elliott, Robert & Qiu, Jinniao & Wei, Wenning, 2022. "Neumann problem for backward SPDEs with singular terminal conditions and application in constrained stochastic control under target zone," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 68-97.
    7. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Working Papers hal-03835948, HAL.
    8. Eyal Neuman & Alexander Schied & Chengguo Weng & Xiaole Xue, 2020. "A central bank strategy for defending a currency peg," Papers 2008.00470, arXiv.org.
    9. Eyal Neuman & Yufei Zhang, 2023. "Statistical Learning with Sublinear Regret of Propagator Models," Papers 2301.05157, arXiv.org.
    10. Eduardo Abi Jaber & Eyal Neuman, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Papers 2211.00447, arXiv.org.

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    More about this item

    Keywords

    Optimal portfolio liquidation; Market impact; Target zone models; Optimal stochastic control; Catalytic superprocess;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation

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