There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify...

Quantifiable, measurable risk is of critical importance when making data-driven decisions in finance and investment management, but what if the generally accepted practice of the investment industry for calculating risk possessed incorrect mathematical assumptions and embedded biases? This piece...