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Arbitrage without borrowing or short selling?

Author

Listed:
  • Mikko S. Pakkanen

    (Imperial College London and CREATES)

  • Jani Lukkarinen

    (University of Helsinki)

Abstract

We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwise Riemann-Stieltjes integral. Our result exemplifies the potential intricacies of formulating economically meaningful self-financing conditions in continuous time, when one leaves the conventional arbitrage-free framework.

Suggested Citation

  • Mikko S. Pakkanen & Jani Lukkarinen, 2016. "Arbitrage without borrowing or short selling?," CREATES Research Papers 2016-13, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2016-13
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    File URL: https://repec.econ.au.dk/repec/creates/rp/16/rp16_13.pdf
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    References listed on IDEAS

    as
    1. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 93-108, February.
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    3. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    4. 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.
    5. Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Short selling; self-financing condition; arbitrage; Riemann-Stieltjes integral; stochastic integral; semimartingale 2010 Mathematics Subject Classification: 60H05; 90G10; 60G44;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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