Analytical phase diagram of the non-linear Chiarella model

Characterize analytically the dynamical phase diagram of the non-linear Chiarella model with cubic fundamentalists' demand f(δ) = κ δ + κ3 δ^3 in the price equation (as defined in Section 2.2), identifying the qualitative regimes and their boundaries in parameter space.

Background

The paper argues that the linear Chiarella model cannot explain empirically observed bimodality in mispricing for several assets, prompting the adoption of a non-linear variant with cubic fundamentalist demand. While the linear model’s stability and bifurcation structure are fully derived, the authors note that the non-linear model exhibits a richer set of behaviors whose full analytical characterization is incomplete.

A complete analytical phase diagram would delineate parameter regions corresponding to qualitatively distinct dynamics (e.g., stability of fixed points, emergence of limit cycles), thereby aligning theoretical predictions with the empirical features such as bimodal mispricing documented across asset classes.