Three theorems with applications to euclidean distance matrices

AbstractIn a recent paper on the theory of Euclidean distance matrices, Gower derived an inequality which characterizes such matrices and challenged his readers to provide a direct proof of this result. The present paper represents the author's response to that challenge

Modeling house price dynamics with heterogeneous speculators

This paper investigates the impact of speculative behavior on house price dynamics. Speculative demand for housing is modeled using a heterogeneous agent approach, whereas ‘real’ demand and housing supply are represented in a standard way. Together, real and speculative forces determine excess demand in each period and house price adjustments. Three alternative models are proposed, capturing in different ways the interplay between fundamental trading rules and extrapolative trading rules, resulting in a 2D, a 3D, and a 4D nonlinear discretetime dynamical system, respectively. While the destabilizing effect of speculative behavior on the model’s steady state is proven in general, the three specific cases illustrate a variety of situations that can bring about endogenous dynamics, with lasting and significant price swings around the ‘fundamental ’ price, as we have seen in many real markets