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We survey a series of models studying financial markets populated by different kinds of (boundedly rational) traders. We show how asset price dynamics qualitatively similar to those of real world, including stylized facts as bubbles and crashes, can be obtained by introducing some regime switching mechanisms. Mathematically, we build piecewise-linear dynamical systems characterized by a particular kind of bifurcation called border-collision bifurcation, leading to complex and unpredictable price dynamics.

Finance, heterogeneous traders, piecewise-linear maps