In the smallest filtration with respect to which a given random time is a stopping time, we represent and characterize local martingales and semimartingales. We then provide necessary and sufficient conditions on the representation of such a semimartingale such that the absence of arbitrage conditions NA_+, NA, NUPBR, or NFLVR hold. One direction of the proof involves explicit constructions of arbitrage opportunities and unbounded profits with bounded risk. The other direction employs a generalized Gronwall—Bellman inequality.

This talk is based on joint work in progress with Martin Herdegen (University of Warwick). Speaker(s): Sebastian Hermann (UM)