The Existence of Absolutely Continuous Local Martingale Measures", Annals of Applied Probability

Abstract. We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for gen-eral admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes. 1.Introduction. In our paper Delbaen and Schachermayer (1994a) we showed that for locally bounded flnite dimensional stochastic price processes S, the existence of an equivalent (local) martingale mea-sure { sometimes called risk neutral measure { is equivalent to a property called No Free Lunch with Vanishing Risk (NFLVR). We also proved that if the set of (local) martingale measure