We discuss some recent developments in the probabilistic analysis of asset price bubbles. Such a bubble is usually described as a local martingale appearing on top of the perceived fundamental value of a liquid asset, defined as the expected sum of future discounted dividends under a given equivalent martingale measure. In this view, either there is a bubble right at the beginning, or there is none  at all. In order to capture the slow birth of a perceived bubble, we study a flow in the space of equivalent martingale measures and the corresponding shifting perception of the fundamental value. This allows us to describe the birth of a bubble as an initial  submartingale which then turns into a supermartingale before it falls back to its initial value zero. The talk will be based on joint work with Francesca Biagini and Sorin Nedelcu.

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