No-arbitrage under additional information for thin semimartingale models

This paper completes the studies undertaken in Aksamit et al. (2017, 2018) [1,2] and Choulli and Deng (2017) [8], where we quantify the impact of a random time on the no-unbounded-profit-with-boundedrisk concept (called NUPBR hereafter) for quasi-left-continuous models and discrete-time market models respectively. Herein, we focus on NUPBR for semimartingale models that live on thin predictable sets only and when the extra information about the random time is added progressively over time. This leads to the probabilistic setting of two filtrations where one filtration contains the other and makes the random time a stopping time. For this framework, we explain how far NUPBR is affected when one stops the model by an arbitrary random time, or when one incorporates in a progressive way an honest time into the model. Furthermore, we show how to construct explicitly some local martingale deflators in the largest filtration for a particular class of models. As a consequence, by combining the current results on the thin case and those of Aksamit et al. (2017, 2018) [1,2], we elaborate universal results for general semimartingale models. (C) 2018 Elsevier B.V. All rights reserved.