title: A financial market model with endogenous fundamental values through imitative behavior.
abstract: In this paper, we propose a financial market model with heterogeneous speculators, i.e., optimistic and pessimistic fundamentalists that, respectively, overestimate and underestimate the true fundamental value due to ambiguity in the stock market, which prevents them from relying on the true fundamental value in their speculations. Indeed, we assume that agents use in its place fundamental values determined by an imitative process. Namely, in forming their beliefs, speculators consider the relative profits realized by optimists and pessimists and update their fundamental values proportionally to those relative profits. Moreover, differently from the majority of the literature on the topic, the stock price is determined by a nonlinear mechanism that prevents divergence issues. For our model, we study, via analytical and numerical tools, the stability of the unique steady state, its bifurcations, as well as the emergence of complex behaviors. We also investigate multistability phenomena, characterized by the presence of coexisting attractors.
authors.affiliation: Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy.
authors.forename: Ahmad
authors.initials: A
authors.lastname: Naimzada
authors.affiliation: Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano, Italy.
authors.forename: Marina
authors.initials: M
authors.lastname: Pireddu