2014/04/01 by Tahir Choulli, Anna Aksamit, Choulli, Tahir +5 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1404.0410
openalex publication_date 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 at 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-tau" local martingale deflators for a large class of initial models (i.e. models in the small filtration) that are already risk-neutralized.