This paper develops the notion of a large type limit (LTL) describing the dynamical behavior of heterogeneous markets with many trader types. It is shown that generic and persistent features of adaptive evolutionary systems with many trader types are well described by the large type limit. Stability, bifurcation routes to instability and strange attractors in a simple evolutionary financial market model are studied. An increase in the "intensity of adaption" or in the diversity of beliefs may lead to deviations from an unstable RE fundamental benchmark and excess volatility. A large evolutionary system may thus become unstable and complicated dynamics may arise when agents become sensitive to small differences in fitness.
This paper formalizes the idea that more hedging instruments may destabilize markets when traders are heterogeneous and adapt their behavior according to experience based reinforcement learning. We investigate three different economic settings, a simple mean-variance asset pricing model, a general equilibrium two-period overlapping generations model with heterogeneous expectations and a noisy rational expectations asset pricing model with heterogeneous information signals. In each setting the introduction of additional Arrow securities can destabilize the market, causing a bifurcation of the steady state to multiple steady states, periodic orbits or even chaotic fluctuations.
We perform a bifurcation analysis of normal-internal resonances in parametrized families of quasi-periodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, called the 'backbone' system; forced, the system is a skew-product flow with a quasiperiodic driving with n basic frequencies. The dynamics of the forced system are simplified by averaging over the orbits of a linearization of the unforced system. The averaged system turns out to have the same structure as in the well-known case of periodic forcing (n = 1); for a real analytic system, the nonintegrable part can even be made exponentially small in the forcing strength. We investigate the persistence and the bifurcations of quasi-periodic n-dimensional tori in the averaged system, filling normal-internal resonance 'gaps' that had been excluded in previous analyses. However, these gaps cannot completely be filled up: secondary resonance gaps appear, to which the averaging analysis can be applied again. This phenomenon of 'gaps within gaps' makes the quasiperiodic case more complicated than the periodic case.
A simple asset pricing model with two types of boundedly rational traders, fundamentalists and chartists, is studied. Fractions of trader types change over time according to evolutionary learning, with chartists conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously and two generic mechanisms are proposed as an explanation: (1) coexistence of a stable steady state and a stable limit cycle, due to a so-called Chenciner bifurcation of the system and (2) intermittency and associated bifurcation routes to strange attractors. Economic intuition as to why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.
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