Inspired by the question of identifying the start time τ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange...

We present a detailed bubble analysis of the Bitcoin to US Dollar price dynamics from January 2012 to February 2018. We introduce a robust automatic peak detection method that classifies price time series into periods of uninterrupted market growth (drawups) and regimes of uninterrupted market...

We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors' beliefs and sentiments. The conditional expected returns...

The financial crisis of 2008, which started with an initially well-defined epicenter focused on mortgage backed securities (MBS), has been cascading into a global economic recession, whose increasing severity and uncertain duration has led and is continuing to lead to massive losses and damage...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the logperiodic power law (LPPL) model has been developed as a...

We introduce the concept of “negative bubbles” as the mirror image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation...

Chapter Summary: We consider the recent financial crisis as an overlapping sequence of interdependent financial bubbles followed by their collapse. Governments and regulatory agencies have made it a prime goal to moderate future crises. Many attempts at financial, economic and social engineering...

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained...