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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 timing of future change points. In particular, we help to explain why previous approaches have systematically overstated the timing of changes in market regime. The list of potential empirical applications is deep and wide ranging, and includes contemporary housing bubbles, the Eurozone crisis and the Crash of 2008.