One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets

We develop a simple financial market model with heterogeneous interacting speculators. The dynamics of our model is driven by a one-dimensional discontinuous piecewise linear map, having two discontinuity points and three linear branches. On the one hand, we study this map analytically and numerically to advance our knowledge about such dynamical systems. In particular, not much is known about discontinuous maps involving three branches. On the other hand, we seek to improve our understanding of the functioning of financial markets. We find, for instance, that such maps can generate complex bull and bear market dynamics.