Perception of Fundamental Values and Financial Market Dynamics: Mathematical Insights from a 2D Piecewise Linear Map

.We develop a simple financial market model in which a market maker adjusts the price with respect to orders placed by chartists and fundamentalists. A novel feature of our model is that fundamentalists optimistically (pessimistically) believe in a relatively high (low) fundamental value when the financial market is increasing (decreasing). As it turns out, the dynamics of our model is driven by a two-dimensional discontinuous piecewise linear map for which we provide an in-depth analytical and numerical investigation. Among other things, we obtain in explicit form the boundaries of the periodicity regions associated with attracting cycles with rotation number \(1/n\) , \(n≥ 3.\) These boundaries correspond to border collision bifurcations of the related cycles. We show that the periodicity regions are organized in a specific period adding structure, and some of the regions may overlap. Several examples of coexisting cycles and their basins of attraction are also presented. Economically, our results offer a new explanation for the boom-bust behavior of actual financial markets.Keywords2D discontinuous piecewise linear mapborder collision bifurcationbifurcation structurefinancial market modelboom-bust cyclesMSC codes37G3537G1537E9937N4091B5591B64