The martingale theory of bubbles studies the existence and characterization of asset price bubbles in continuous time and continuous trading economies under both the no arbitrage (no free lunch vanishing risk) and no dominance hypotheses. We review this theory, with an emphasis on understanding...

Financial bubbles and crashes have repeatedly caused economic turmoil notably but not only during the 2008 financial crisis. However, both in the popular press as well as scientific publications, the meaning of bubble is sometimes unspecified. Due to the multitude of bubble definitions, we...