Exploiting Arbitrage Requires Short Selling

Eckhard Platen and Stefan Tappe

Chapter 21 in Peter Carr Gedenkschrift:Research Advances in Mathematical Finance, 2023, pp 725-752 from World Scientific Publishing Co. Pte. Ltd.

Abstract: We show that in a financial market given by semimartingales, an arbitrage opportunity, provided it exists, can only be exploited through short selling. This finding provides a theoretical basis for differences in regulation for financial services providers that are allowed to go short and those without short sales. The privilege to be allowed to short sell gives access to potential arbitrage opportunities, which creates by design a bankruptcy risk.

Keywords: Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures (search for similar items in EconPapers)
JEL-codes: C02 C6 (search for similar items in EconPapers)
Date: 2023
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