Essays on artificial stock market methods

This dissertation proposes a two-risky-asset Artificial Stock Market Model and investigates its applications in financial markets. In the first essay, this model is applied to the stock market. Simulation results show that within some range of the parameters, the model can replicate many stylized facts of real financial data and some financial anomalies. This essay also finds that the dynamics of the model and the simulated results can be explained well by two approximation equations: the bubble pricing equation and the mean difference equation of the market share. The second essay applies the noise trader version of this model to the foreign exchange market and aims at solving the equilibria selection dilemma in the context of Kareken and Wallace (1981). The simulation results show that if agents have full memory, the average portfolio fraction will converge and the initial equilibrium that it converges to is history dependent. However under the lasting evolutionary pressure brought by the noise trader, the asymptotical outcome will be history independent. The model will converge to the neighborhood of an equilibrium with agents equally putting their savings into two currencies. If the agents do not have full memory, the foreign exchange market will show periodic crises. Before and after a market crisis, the exchange rate will converge to different stationary equilibria. A mean difference equation of the average portfolio fraction is also given to describe the dynamics of the model. The third essay aims at revealing the role played by the self-referential process inside the artificial stock models, and studying how it is related to the model performance. Three potential dangers that can make a GA learning model degenerate to a pure numerical optimization process are identified. It is also found that although the strength of the self-referential process may not change the convergence property of a GA model, it may lead to substantial differences in the model dynamics before the convergence is achieved.