Type of Document Dissertation Author Culham, Andrew James Author's Email Address email@example.com URN etd-07062007-135531 Title Asset Pricing in a Lucas Framework with Boundedly Rational, Heterogeneous Agents Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Alec Kercheval Committee Co-Chair Paul Beaumont Committee Co-Chair David Kopriva Committee Member Don Schlagenhauf Committee Member Yevgeny Goncharov Committee Member Keywords
- Asset Pricing
- Boundedly Rational
- Non Equilibrium
- Lucas Model
Date of Defense 2007-06-29 Availability unrestricted AbstractThe standard dynamic general equilibrium model of financial markets does a poor job of explaining the empirical facts observed in real market data. The common assumptions of homogeneous investors and rational expectations equilibrium are thought to be major factors leading to this poor performance. In an attempt to relax these assumptions, the literature has seen the emergence of agent-based computational models where artificial economies are populated with agents who trade in stylized asset markets. Although they offer a great deal of flexibility, the theoretical community has often criticized these agent-based models because the agents are too limited in their analytical abilities.
In this work, we create an artificial market with a single risky asset and populate it with fully optimizing, forward looking, infinitely lived, heterogeneous agents. We restrict the state space of our agents by not allowing them to observe the aggregate distribution of wealth so they are required to compute their conditional demand functions while simultaneously learning the equations of motion for the aggregate state variables. We develop an efficient and flexible model code that can be used to explore a wide number of asset pricing questions while remaining consistent with conventional asset pricing theory. We validate our model and code against known analytical solutions as well as against a new analytical result for agents with differing discount rates.
Our simulation results for general cases without known analytical solutions show that, in general, agents' asset holdings converge to a steady-state distribution and the agents are able to learn the equilibrium prices despite the restricted state space. Further work will be necessary to determine whether the exceptional cases have some fundamental theoretical explanation or can be attributed to numerical issues. We conjecture that convergence to the equilibrium is global and that the market-clearing price acts to guide the agents' forecasts toward that equilibrium.
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