Evolution and Time Horizons in an Agent-Based Stock Market

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Abstract
Recent research has shown the importance of time horizons in models of learning in finance. The dynamics of how agents adjust to believe that the world around them is stationary may be just as crucial in the convergence to a rational-expectations equilibrium as getting parameters and model specifications correct in the learning process. This paper explores the process of this evolution in learning and time horizons in a simple agent-based financial market. Trading is done in a market with a single stock in finite supply, paying a stochastic dividend. A risk free asset is available in infinite supply. Agents maximize an infinite-horizon time-separable utility function in each period's consumption. They are required to select from a set of given forecasting/trading rules optimized to past data. Heterogeneity is introduced through the time horizon that they believe is relevant to use in deciding over trading rules. Long horizon agents build relative performance measures looking back into the distant past, while those with short horizons believe that only recent measures of performance are useful for decision making. The price of the risky asset is set to balance current agent demand with its fixed supply at each period. Once the price is endogenously determined, returns are calculated and dividends paid. Agents make consumption decisions and wealth is calculated. Relative wealth affects the market in two ways. First, wealthier individuals are able to move prices by larger amounts. Second, evolution takes place in which less wealthy agents are dropped out of the market and replaced with new ones drawn according to current wealth levels. The horizon lengths of wealthier agents are given more weight in the generation of new agents. The primary objectives of this paper are to understand better the convergence properties of learning with heterogeneous horizons. Several benchmark cases are explored in which a stationary rational-expectations equilibrium exists, and agents sh
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