Before revision:  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 .
After revision:  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 , while the second main result characterizes the honest times that preserve the NUPBR property .