No-arbitrage up to random horizon for quasi-left-continuous models

Anna Aksamit, Tahir Choulli (), Jun Deng and Monique Jeanblanc
Additional contact information
Anna Aksamit: University of Oxford
Tahir Choulli: University of Alberta
Jun Deng: University of International Business and Economics
Monique Jeanblanc: Université d’Evry-Val-d’Essonne

Finance and Stochastics, 2017, vol. 21, issue 4, No 7, 1103-1139

Abstract: Abstract This paper studies the impact, on no-arbitrage conditions, of stopping the price process at an arbitrary random time. As price processes, we consider the class of quasi-left-continuous semimartingales, i.e., semimartingales that do not jump at predictable stopping times. We focus on the condition of no unbounded profit with bounded risk (called NUPBR), also known in the literature as no arbitrage of the first kind. The first principal result describes all the pairs of quasi-left-continuous market models and random times for which the resulting stopped model fulfils NUPBR. Furthermore, for a subclass of quasi-left-continuous local martingales, we construct explicitly martingale deflators, i.e., strictly positive local martingales whose product with the price process stopped at a random time is a local martingale. The second principal result characterises the random times that preserve NUPBR under stopping for any quasi-left-continuous model. The analysis carried out in the paper is based on new stochastic developments in the theory of progressive enlargements of filtrations.

Keywords: No unbounded profit with bounded risk; No arbitrage; Random horizon; Informational arbitrage; Deflators; Quasi-left-continuous semimartingales; Progressive enlargement of filtration; Stochastic calculus; 91B44; 91B70; 91G40; 60G48; 60G51; 60G57 (search for similar items in EconPapers)
JEL-codes: D80 D81 D82 G14 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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DOI: 10.1007/s00780-017-0337-3

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