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Arbitrage without borrowing or short selling?

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  • Jani Lukkarinen
  • Mikko S. Pakkanen

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

  • Jani Lukkarinen & Mikko S. Pakkanen, 2016. "Arbitrage without borrowing or short selling?," Papers 1604.07690, arXiv.org, revised Oct 2016.
    • Handle: RePEc:arx:papers:1604.07690
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    References listed on IDEAS

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    5. Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
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