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


Coculescu, Delia; Jeanblanc, Monique (2019). Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices. Finance and Stochastics, 23(2):397-421.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Finance
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:2019
Deposited On:16 Jan 2020 08:17
Last Modified:29 Jul 2020 12:39
Publisher:Springer
ISSN:0949-2984
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s00780-019-00386-3
Official URL:https://link.springer.com/article/10.1007/s00780-019-00386-3
Other Identification Number:merlin-id:17736

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