Financial Asset Price Bubbles under Model Uncertainty

18 May 2017
Francesca Biagini

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.

  • Mathematical and Computational Finance Seminar