Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers
AbstractThis paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using a geometric decay processes (GDP) - the expected mean and variance are estimated as a geometric weighted average of past observations - with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics of the model can be characterized with respect to the length of memory window and the memory decay rate of the learning GPD. The dynamics of such heterogeneous learning processes and capability of producers' learning are discussed. It is found that the learning memory decay rate of the GDP of heterogeneous producers plays a complicated role on the pricing dynamics of the nonlinear cobweb model. In general, an increase of the memory decay rate plays stabilizing role on the local stability of the steady state price when the memory is infinite, but this role becomes less clear when the memory is finite. It shows a double edged effect of the heterogeneity on the dynamics. It is shown that (quasi)periodic solutions and strange (or even chaotic) attractors can be created through Neimark-Hopf bifurcation when the memory is infinite and through flip bifucation as well when the memory is finite.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 108.
Date of creation: 01 Sep 2003
Date of revision:
cobweb model; heterogeneity; bounded rationality; geometric decay learning dynamics; bifurcations;
Other versions of this item:
- Peiyuan Zhu & Carl Chiarella & Tony He, 2003. "Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers," Computing in Economics and Finance 2003 31, Society for Computational Economics.
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
- D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
- E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-08-16 (All new papers)
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