We present a dynamic Rational Expectations (RE) bubble model of prices with the intention to evaluate it on optimal investment strategies applied to Bitcoin. Our bubble model is defined as a geometric Brownian motion combined with separate crash (and rally) discrete jump distributions associated...

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...

Building on the notion that bubbles are transient self-fulfilling prophecies created by positive feedback mechanisms, we construct the simplest continuous price process whose expected returns and volatility are functions of momentum only. The momentum itself is measured by a simple continuous...

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space...

At odds with the common “rational expectations” framework for bubbles, economists like Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational behavior, ambiguous information or certain limits to arbitrage are essential drivers for bubble phenomena and financial...

Using the mechanics of creep in material sciences as a metaphor, we present a general framework to understand the evolution of financial, economic and social systems and to construct scenarios for the future. In a nutshell, highly non-linear out-of-equilibrium systems subjected to exogenous...