No-arbitrage under a class of honest times.

Summary This paper quantifies the interplay between the no-arbitrage notion of no-unbounded-profit-with-bounded-risk (NUPBR hereafter) and additional progressiveinformation generated by a randomtime. This study complements the one of Aksamit et al. in which the authors have studied similar topics for the case of stopping at the randomtime instead, while herein we deal with the part after the occurrence of the randomtime. Given that all the literature, up to our knowledge, proves that NUPBR 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 NUPBR can be preserved for some models. For these honest times, we obtain two principal results. The first result characterizes the pairs of initial market and honest time for which the resulting model preserves NUPBR, while the second result characterizes honest times that do not affect NUPBR of any quasi-left-continuous model (i.e., model in which the assets’ price process has no predictable jump times). Furthermore, we construct explicitly local martingale deflators for a large class of models.