Abstract. In this paper we propose a model of asset prices consistent with the no-arbitrage principle but allowing for the existence of "bubbles". The structure of bubbles is explicitely characterized and we show that, for example, they may be of either sign. Furthermore, we discuss the existence of bubbles under alternative definitions of absence of arbitrage opportunitites.

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 allows for a very clear representation which allows, as in Breeden and Litzenberger [7], to extract the implied probability.principle of modern financial theory, i.e. risk neutral pricing. Although many an author inclines to believe that this basic principle rests on the simple tenet asserting that markets populated by rational economic agents cannot admit arbitrage opportunities, the proof of this claim, the fundamental theorem of asset pricing, has long been a challenge for mathematical economists, from Kreps [26] to Delbaen and Schachermayer [14]. In fact it requires a much more stringent condition than absence of arbitrage in which probability is needed to induce an appropriate topology.

Abstract. In this paper we propose a model of …nancial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite …nite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure, based on some new results on …nitely additive measures. From this representation we derive an exact decomposition of the rsik premiu as the sum of the correlation of returns with the market price of risk and an additional term, the purely …nitely additive premium, related to the jumps of the return process. We also discuss the implications of the absence of free lunches.

We prove an L ∞ version of Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets in which asset prices are a continuous R d valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.