We present an extension of the Johansen-Ledoit-Sornette (JLS) model to include an additional pricing factor called the ``Zipf factor'', which describes the diversification risk of the stock market portfolio. Keeping all the dynamical characteristics of a bubble described in the JLS model, the...

This paper provides a mapping from portfolio risk diversification into the pairwise correlation between portfolios. In a finite market of uncorrelated assets, portfolio risk is reduced by increasing diversification. However, higher the diversification level, the greater is the overlap between...