Asset pricing in an imperfect world

In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no-arbitrage property. We show that prices are coherent if and only if the set of pricing measures is non-empty, i.e., if pricing by expectation is possible. We then obtain a decomposition of coherent prices highlighting the role of bubbles. Eventually, we show that under very weak conditions, the coherent pricing of options implies a very clear representation which permits, as in Breeden and Litzenberger (J Bus 51:621-651, 1978), to extract the implied probability.