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  and .
 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.
 Biagini, F., Mancin, J.,
Financial Asset Price Bubbles under Model
Uncertainty, Preprint, 2016.
- Mathematical and Computational Finance Seminar