In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected...

We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate...

We explore the taxonomy of cryptocurrencies and integrate our analysis with traditional ways of understanding financial assets. We thus classify cryptocurrencies using the time series and distributional properties of returns. Cryptocurrencies appear inherently speculative in nature. The result...