Arbitrage without borrowing or short selling?

Mikko S. Pakkanen () and Jani Lukkarinen ()
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Mikko S. Pakkanen: Imperial College London and CREATES, Postal: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Jani Lukkarinen: University of Helsinki, Postal: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsingin yliopisto, Finland

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Short selling; self-financing condition; arbitrage; Riemann-Stieltjes integral; stochastic integral; semimartingale 2010 Mathematics Subject Classification: 60H05; 90G10; 60G44 (search for similar items in EconPapers)
JEL-codes: C22 G11 G14 (search for similar items in EconPapers)
Pages: 13
Date: 2016-04-26
New Economics Papers: this item is included in nep-fmk
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