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The standard Lucas asset pricing model makes two common assumptions of homogeneous agents and rational expectations equilibrium. However, these assumptions are unrealistic for real financial markets. In this work, we relax these assumptions and establish a Lucas type agent-based asset pricing model. We create an artificial economy with a single risky asset and populate it with heterogeneous, boundedly rational, utility maximizing, infinitely lived and forward looking agents. We restrict agents' information by allowing them to use only available information when they make optimal choices. With independent, identically distributed market returns, agents are able to compute their policy functions and the equilibrium pricing function with Duffie's method (Duffie, 1988) without perfect information about the market. When agents are out of equilibrium, they simultaneously compute their policy functions with predictive pricing functions and use adaptive learning schemes to learn the motion of the correct pricing function. Agents are able to learn the correct equilibrium pricing function with certain risk and learning parameters. In some other cases, the market price has excess volatility and the trading volume is very high. Simulations of the market behavior show rich dynamics, including a whole cascade from period doubling bifurcations to chaos. We apply the full families theory (De Melo and Van Strien, 1993) to prove that the rich dynamics do not come from numerical errors but are embedded in the structure of our dynamical system.
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Paul M. Beaumont, Professor Co-Directing Dissertation; Alec N. Kercheval, Professor Co-Directing Dissertation; Milton Marquis, University Representative; Mike Mesterton-Gibbons, Committee Member; Warren D. Nichols, Committee Member.
Florida State University
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