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Modeling Liquidity Effects In Discrete Time

Author

Listed:
  • Umut Çetin
  • L. C. G. Rogers

Abstract

We study optimal portfolio choices for an agent with the aim of maximising utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox-Ross-Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.
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Suggested Citation

  • Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
  • Handle: RePEc:bla:mathfi:v:17:y:2007:i:1:p:15-29
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    References listed on IDEAS

    as
    1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
    2. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    3. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    4. 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..
    5. Cuoco, Domenico & Cvitanic, Jaksa, 1998. "Optimal consumption choices for a 'large' investor," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 401-436, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dylan Possamai & Nizar Touzi & H. Mete Soner, 2012. "Large liquidity expansion of super-hedging costs," Papers 1208.3785, arXiv.org, revised Apr 2015.
    2. Jinqiang Yang & Zhaojun Yang, 2012. "Arbitrage-free interval and dynamic hedging in an illiquid market," Quantitative Finance, Taylor & Francis Journals, vol. 13(7), pages 1029-1039, May.
    3. Teemu Pennanen, 2008. "Arbitrage and deflators in illiquid markets," Papers 0807.2526, arXiv.org, revised Apr 2009.
    4. Paolo Guasoni & Mikl'os R'asonyi, 2015. "Hedging, arbitrage and optimality with superlinear frictions," Papers 1506.05895, arXiv.org.
    5. repec:spr:compst:v:71:y:2010:i:3:p:551-585 is not listed on IDEAS
    6. Yan Dolinsky & Halil Mete Soner, 2011. "Duality and Convergence for Binomial Markets with Friction," Papers 1106.2095, arXiv.org.
    7. Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 551-585, June.
    8. Kraft, Holger & Kühn, Christoph, 2011. "Large traders and illiquid options: Hedging vs. manipulation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1898-1915.
    9. Henry Schellhorn & Ran Zhao, 2016. "A String Model of Liquidity in Financial Markets," Papers 1608.05900, arXiv.org.
    10. Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
    11. repec:wsi:ijtafx:v:20:y:2017:i:05:n:s0219024917500261 is not listed on IDEAS
    12. c{C}au{g}{i}n Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org, revised Sep 2017.
    13. 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.
    14. Terje Lensberg & Klaus Reiner Schenk-Hopp'e, 2013. "Hedging without sweat: a genetic programming approach," Papers 1305.6762, arXiv.org.
    15. Alexandre F. Roch, 2008. "Liquidity Risk, Price Impacts and the Replication Problem," Papers 0812.2440, arXiv.org, revised Dec 2009.

    More about this item

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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