Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices

Delia Coculescu () and Monique Jeanblanc ()
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Delia Coculescu: University of Zurich
Monique Jeanblanc: Université d’Evry Val d’Essonne

Finance and Stochastics, 2019, vol. 23, issue 2, No 4, 397-421

Abstract: Abstract Under short-sales prohibitions, no free lunch with vanishing risk (NFLVRS) is known to be equivalent to the existence of an equivalent supermartingale measure for the price process (Pulido in Ann. Appl. Probab. 24:54–75, 2014). We give a necessary condition for the drift of a price process to satisfy NFLVRS. For two given price processes, we introduce the concept of fundamental supermartingale measure, and when a certain condition necessary for the construction of this fundamental supermartingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., two prices that coincide at a bounded random time.

Keywords: Equivalent supermartingale measures; No free lunch with vanishing risk; Short-sales constraints; Converging asset prices; 60G46; 91B70; 91G99 (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-019-00386-3

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