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Hedging and portfolio optimization in illiquid financial markets

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  • Bank, Peter
  • Baum, Dietmar

Abstract

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter dependent semimartingales, and its mathematical analysis relies on the non-linear integration theory of such semimartingale families. The Itô-Wentzell formula is used to prove absence of arbitrage for the large investor, and using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.

Suggested Citation

  • Bank, Peter & Baum, Dietmar, 2002. "Hedging and portfolio optimization in illiquid financial markets," SFB 373 Discussion Papers 2002,53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200253
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    References listed on IDEAS

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    1. Robert A. Jarrow, 2008. "Market Manipulation, Bubbles, Corners, and Short Squeezes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 6, pages 105-130, World Scientific Publishing Co. Pte. Ltd..
    2. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    3. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    4. K. Ronnie Sircar & George Papanicolaou, 1998. "General Black-Scholes models accounting for increased market volatility from hedging strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 45-82.
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    6. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    7. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
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    Cited by:

    1. 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.

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