This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk , NUPBR hereafter) after a specific random time. This study completes the one of Aksamit et al. \mbox{%DIFAUXCMD aksamit/choulli/deng/jeanblanc ]  the part after the random time under consideration. We restrict our attention to honest times, and we characterize the pairs of market and honest time for which the resulting model preserves the NUPBR property . Furthermore, we characterize the honest times that preserve the NUPBR property . These findings are essentially based on new stochastic results that are interesting in themselves. Furthermore, we construct explicitly  local martingale deflators for a large class of processes .
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 .
R
addresses the question of
quantifies the interplay between the
R
(precisely
notion of
R
,
(
R
after a specific
and additional information generated by a
R
completes
complements
R
et al. \mbox{%DIFAUXCMD aksamit/choulli/deng/jeanblanc
/Choulli/Deng/Jeanblanc
A
1
A
in which the authors studied similar topics for the case of stopping at the random time instead, while herein we are concerned with
R
random time under consideration. We restrict our attention to honest times, and we characterize the pairs of
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
R
. Furthermore, we characterize the
, while the second main result characterizes the
R
. These findings are essentially based on new stochastic results that are interesting in themselves.
for any quasi-left continuous model.
A
"the-after-tau"
R
processes
initial models (i.e. models in the small filtration) that are already risk-neutralized