Analytical stationary distribution of mispricing in the non-linear Chiarella model

Derive the analytical stationary probability density of the mispricing process δ = P − V for the non-linear Chiarella model with cubic fundamentalists' demand f(δ) = κ δ + κ3 δ^3 (as defined in Section 2.2).

Background

To assess bimodality in mispricing, the authors rely on nonparametric tests and simulation because a closed-form stationary distribution is not available for the non-linear model. This limits direct analytical evaluation of the conditions under which mispricing is bimodal.

Obtaining the stationary density would provide a theoretical foundation for the empirical and numerical findings, enabling explicit characterization of modality and more precise links between parameter values and distributional features.