When any bubble burst, not only many investors suffer directly, but it also affects the entire economy. Therefore, it is important to develop an early warning using optimization-supported tools. Since there is not yet really satisfactory theory related to bubbles, this book firstly contribute to the theoretical understanding of financial bubbles. Empirical results can also help understanding the dynamics of the bubbles. We generate a volume-based index via minimum-volume covering ellipsoid clustering method, and to visualize these ellipsoids, we utilize Radon transform (RT) from the theory of the inverse problems. We have observed that when the bubble-burst time approaches , the volumes of the ellipsoids gradually decreases and, correspondingly, the figures obtained by RT are becoming more brilliant, i.e., more strongly warning. The risk management departments at the banks may use theoretical and empirical results of our investigations to manage their market risk. Also, Central Banks and policy makers could benefit from our approach to monitor their risk levels and compute the risk associated with various economic factors. This could prevent from financial and economics crises.