Non-Arbitrage under a Class of Honest TimesReport as inadecuate

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* Corresponding author 1 LaMME - Laboratoire de Mathématiques et Modélisation d-Evry 2 University of Oxford Oxford 3 University of Alberta Edmonton 4 College of Engineering Beijing 5 UEVE - Université d-Évry-Val-d-Essonne

Abstract : This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk NUPBR hereafter and additional information generated by a random time. This study complements the one of Aksamit-Choulli-Deng-Jeanblanc 1 in which the authors studied similar topics for the case of stopping with the random time instead, while herein we are concerned with the part after the occurrence of the random time. Given that all the literature —up to our knowledge— proves that the NUPBR notion is always violated after honest times that avoid stopping times in a continuous filtration, herein we propose a new class of honest times for which the NUPBR notion can be preserved for some models. For this family of honest times, we elaborate two principal results. The first main result characterizes the pairs of initial market and honest time for which the resulting model preserves the NUPBR property, while the second main result characterizes the honest times that preserve the NUPBR property for any quasi-left continuous model. Furthermore , we construct explicitly - the-after-τ - local martingale deflators for a large class of initial models i.e.,models in the small filtration that are already risk-neutralized.

Author: Anna Aksamit - Tahir Choulli - Jun Deng - Monique Jeanblanc -



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