We study the concept of financial bubble under model uncertainty. We suppose the agent to be endowed with a family Q of local martingale measures for the underlying discounted asset price. The priors are allowed to be mutually singular to each other. One fundamental issue is the definition of a well-posed concept of robust fundamental value of a given financial asset.

Since in this setting we have no linear pricing system, we choose to describe robust fundamental values through superreplication prices. To this purpose, we investigate a dynamic version of robust superreplication, which we use to introduce the notions of bubble and robust fundamental value in a consistent way with the existing literature in the classical case of one prior.

This talk is based on the works [1] and [2].

[1] Biagini, F., Föllmer, H. and Nedelcu, S. Shifting martingale measures and the slow birth of a bubble as a submartingale, Finance and Stochastics: Volume 18, Issue 2, Page 297-326, 2014.

[2] Biagini, F., Mancin, J., Financial Asset Price Bubbles under Model Uncertainty, Preprint, 2016.