Heterogeneous beliefs and routes to chaos in a simple asset pricing model

Arifovich, 1994, Genetic algorithm learning and the cobweb model, Journal of Economic Dynamics and Control, 18, 3, 10.1016/0165-1889(94)90067-1 Arifovich, 1995, Genetic algorithms and inflationary economies, Journal of Monetary Economics, 36, 219, 10.1016/0304-3932(95)01203-7 Arrowsmith, D.K., Place, C.M., 1994. An Introduction to Dynamical Systems. Cambridge University Press, Cambridge. Arthur, W.B., Holland, J.H., LeBaron, B., Palmer, R., Taylor, P., 1996. Asset pricing under endogenous expectations in an artificial stock market. In: Arthur, W., Lane, D., Durlauf, S. (Eds.), The Economy as an Evolving Complex System: II. Addison-Wesley, Redwood City, CA, forthcoming. Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M., 1980a. Lyapunov characteristic exponents for smooth dynamical systems; a method for computing all of them. Part 1: Theory. Meccanica 15, 9–20. Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M., 1980b. Lyapunov characteristic exponents for smooth dynamical systems; a method for computing all of them. Part 2: Numerical application. Meccanica 15, 21–30. Brock, 1986, Distinguishing random and deterministic systems. Abridged version, Journal of Economic Theory, 40, 168, 10.1016/0022-0531(86)90014-1 Brock, 1993, Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance, Estudios Económicos, 8, 3 Brock, W.A., 1995. Asset Price Behavior in Complex Environments. In: Arthur, W., Lane, D., Durlauf, S. (Eds.), The Economy as an Evolving Complex System: II. Addison-Wesley, Redwood City, CA. Brock, W.A., de Fontnouvelle, P., 1996. Expectational diversity in monetary economics. University of Wisconsin, SSRI working paper 9624, forthcoming in Journal of Economic Dynamics and Control. Brock, W.A., Hommes, C.H., 1997a. A rational route to randomness. Econometrica, 65, 1059–1095. Brock, W.A., Hommes, C.H., 1997b. Models of complexity in economics and finance. In: Heij, C., Schumacher, J.M., Hanzon, B., Praagman, C. (Eds.), System Dynamics in Economic and Financial Models. Wiley, New York, Chapter 1, pp. 3–44. Brock, W.A., Hommes, C.H., 1997c. Adaptive beliefs and the emergence of complex dynamics in asset pricing models. Working Paper, Department of Economics, University of Wisconsin, in preparation. Brock, 1992, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance, 47, 1731, 10.2307/2328994 Brock, W.A., LeBaron, B., 1995. A structural model for stock return volatility and trading volume. Review of Economics and Statistics. Bullard, J., Duffy, J., 1994. Using genetic algorithms to model the evolution of heterogeneous beliefs, Working Paper. Chiarella, 1992, The dynamics of speculative behaviour, Annals of Operations Research, 37, 101, 10.1007/BF02071051 Day, 1990, Bulls, bears and market sheep, Journal of Economic Behaviour and Organization, 14, 299, 10.1016/0167-2681(90)90061-H Dacorogna, 1995, Heterogeneous real-time trading strategies in the foreign exchange market, European Journal of Finance, 1, 383, 10.1080/13518479500000026 DeBondt, W.F.M., Thaler, R.H., 1985. Does the stock market overreact? Journal of Finance 40, 793–808 DeGrauwe, P., Dewachter, H., Embrechts, M., 1993. Exchange Rate Theory. Chaotic Models of Foreign Exchange Markets. Blackwell, Oxford. DeLong, 1990, Noise trader risk in financial markets, Journal of Political Economy, 98, 703, 10.1086/261703 Eckmann, 1985, Ergodic theory of chaos and strange attractors, Reviews of Modern Physics, 57, 617, 10.1103/RevModPhys.57.617 Evans, G.W., Honkapohja, S., 1997. Learning Dynamics. In: Taylor, J., Woodford, M. (Eds.), Handbook of Macroeconomics. Falconer, K., 1990. Fractal Geometry. Mathematical Foundations and Applications. Wiley, Chichester. Frankel, 1988, Chartists, fundamentalists and the demand for dollars, Greek Economic Review, 10, 49 Friedman, M., 1953. The case for flexible exchange rates. In: Essays in Positive Economics. Univ. Chicago Press, Chicago. Goeree, J., 1996. Applications of Discrete Choice Models. Ph.D. Thesis, Department of Economics, University of Amsterdam. Guckenheimer, J., Holmes, P., 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York. Haltiwanger, 1985, Rational expectations and the limits of rationality: an analysis of heterogeneity, American Economic Review, 75, 326 Hommes, C.H., 1991. Chaotic Dynamics in Economic Models. Some Simple Case-Studies. Wolters-Noordhoff, Groningen. Hommes, 1995, A reconsideration of Hicks non-linear trade cycle model, Structural Change and Economic Dynamics, 6, 435, 10.1016/0954-349X(95)00032-I Krusell, Smith, 1996. Rules of thumb in macroeconomic equilibrium. A quantitative analysis. Journal of Economic Dynamics and Control 20, 527–558. Kurz, M., 1994a. On rational belief equilibria. Economic Theory 4, 859–876. Kurz, M., 1994b. On the structure and diversity of rational beliefs. Economic Theory 4, 877–900. Kurz, M., 1994c. Asset prices with rational beliefs. Manuscript Stanford University. Kuznetsov, Y.A., 1995. Elements of Applied Bifurcation Theory. Springer, New York. LeBaron, B., 1995. Experiments in evolutionary finance. In: Arthur, W., Lane, D., Durlauf, S. (Eds.), The Economy as an Evolving Complex System: II. Addison-Wesley, Redwood City, CA. Lucas, 1978, Asset prices in an exchange economy, Econometrica, 46, 1426, 10.2307/1913837 Lux, T., 1995. Herd behaviour, bubbles and crashes. The Economic Journal 105, 881–896. Marimon, R., 1997. Learning from learning in economics. In: Kreps, D.M., Wallis, K.F. (Eds.), Advances in Economics and Econometrics: Theory and Applications, vol. I, Proc. 7th World Congress of the Econometric Society. Cambridge University Press, Cambridge. Marimon, 1989, Money as medium of exchange with artificially intelligent agents, Journal of Economic Dynamics and Control, 14, 329, 10.1016/0165-1889(90)90025-C Medio, A., 1992. Chaotic Dynamics. Theory and Applications to Economics. Cambridge University Press, Cambridge. Nelson, 1992, Filtering and forecasting with misspecified ARCH models I: Getting the right variance with the wrong model, Journal of Econometrics, 51, 61, 10.1016/0304-4076(92)90065-Y Palis, J., Takens, F., 1993. Hyperbolicity & Sensitive Chaotic Dynamics at Homoclinic Bifurcations. Cambridge University Press, Cambridge. Sargent, T.J., 1993. Bounded Rationality in Macroeconomics, Oxford University Press, New York. Sethi, 1996, Endogenous regime switching in speculative markets, Structural Change and Economic Dynamics, 7, 99, 10.1016/0954-349X(95)00040-T Sprott, J.C., Rowlands, G., 1992. Chaos Data Analyzer. IBM PC version 1.0, American Institute of Physics, New York. Thaler, R., 1994. Quasi Rational Economics. Russell Sage Foundation, New York. Timmermann, 1993, How learning in financial markets genetates excess volatility and predictability in stock prices, Quarterly Journal of Economics, 108, 1135, 10.2307/2118462 Timmermann, 1996, Excessive volatility and predictability of stock prices in autoregressive dividend models with learning, Review of Economic Studies, 63, 523, 10.2307/2297792 Vilder, de R.G., 1995. Endogenous Business Cycles. Tinbergen Institute Research Series 96, University of Amsterdam. Vilder, de R.G., 1996. Complicated endogenous business cycles under gross substitutability. Journal of Economic Theory. Zeeman, 1974, The unstable behavior of stock exchange, Journal of Mathematical Economics, 1, 39, 10.1016/0304-4068(74)90034-2