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Type of Document Dissertation Author Guan, Yuanying URN etd-07252011-113003 Title Asset Market Dynamics of Heterogeneous Agent Models with Learning Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Alec Kercheval Committee Chair Paul Beaumont Committee Co-Chair Mike Mesterton-Gibbons Committee Member Warren Nichols Committee Member Milton Marquis University Representative Keywords
- Heterogeneous Agent Model
- Chaos
- Economic Dynamics
Date of Defense 2011-06-30 Availability unrestricted Abstract The standard Lucas asset pricing model makes two common assumptions of homogeneousagents 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.
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