A stochastic model for speculative bubbles

Abstract:

“One commonly says that the creation of speculative bubbles is  the
consequence of two phenomenons: the self-reinforcing effect of the investors
and  the  tendency of these investors to follow the forecasting rule which
consists in deciding that the price will increase  if it has (strongly) increased in the past. Following these two rules,
we build a model for speculative bubbles which is a  Gaussian two-dimensional
“turning” diffusion.

Then, the main objective of the work is to obtain some sharp bounds for the time
of return to a given price.

In our main results, we prove with both spectral and probabilistic methods that
the rate of return  is proportional to the rotation frequency of the
deterministic model associated with the diffusion.

I will end the talk by some open questions on the quasi-stationary distribution
related to the problem and on the statistical estimation of the parameters of
the model. This talk is based on a joint work with Sebastien Gadat and Laurent
Miclo.”

Posted on Oct 11, 2013 in Seminars, Stochastic Modeling