Heterogeneous beliefs and routes to chaos in a simple asset pricing model. (English) Zbl 0913.90042

Summary: This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their ‘beliefs’ in each period in a boundedly rational way, according to a ‘fitness measure’ such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (‘rational animal spirits’). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.


91B62 Economic growth models
91B24 Microeconomic theory (price theory and economic markets)
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[1] Arifovich, J., Genetic algorithm learning and the cobweb model, Journal of Economic Dynamics and Control, 18, 3-28 (1994)
[2] Arifovich, J., Genetic algorithms and inflationary economies, Journal of Monetary Economics, 36, 219-243 (1995)
[7] Brock, W. A., Distinguishing random and deterministic systems. Abridged version, Journal of Economic Theory, 40, 168-195 (1986) · Zbl 0616.62125
[8] Brock, W. A., Pathways to randomness in the economy: emergent nonlinearity and chaos in economics and finance, Estudios Económicos, 8, 3-55 (1993)
[14] Brock, W. A.; Lakonishok, J.; LeBaron, B., Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance, 47, 1731-1764 (1992)
[17] Chiarella, C., The dynamics of speculative behaviour, Annals of Operations Research, 37, 101-123 (1992) · Zbl 0777.90008
[18] Day, R. H.; Huang, W., Bulls, bears and market sheep, Journal of Economic Behaviour and Organization, 14, 299-329 (1990)
[19] Dacorogna, M. M.; Müller, U. A.; Jost, C.; Pictet, O. V.; Olsen, R. B.; Ward, J. R., Heterogeneous real-time trading strategies in the foreign exchange market, European Journal of Finance, 1, 383-403 (1995)
[22] DeLong, J. B.; Shleifer, A.; Summers, L. H.; Waldmann, R. J., Noise trader risk in financial markets, Journal of Political Economy, 98, 703-738 (1990)
[23] Eckmann, J.-P.; Ruelle, D., Ergodic theory of chaos and strange attractors, Reviews of Modern Physics, 57, 617-656 (1985) · Zbl 0989.37516
[26] Frankel, J. A.; Froot, K. A., Chartists, fundamentalists and the demand for dollars, Greek Economic Review, 10, 49-102 (1988)
[30] Haltiwanger, J.; Waldmann, M., Rational expectations and the limits of rationality: an analysis of heterogeneity, American Economic Review, 75, 326-340 (1985)
[32] Hommes, C. H., A reconsideration of Hicks non-linear trade cycle model, Structural Change and Economic Dynamics, 6, 435-459 (1995)
[39] Lucas, R. E., Asset prices in an exchange economy, Econometrica, 46, 1426-1446 (1978)
[42] Marimon, R.; McGrattan, E.; Sargent, T., Money as medium of exchange with artificially intelligent agents, Journal of Economic Dynamics and Control, 14, 329-373 (1989) · Zbl 0698.90014
[44] Nelson, D., Filtering and forecasting with misspecified ARCH models I: Getting the right variance with the wrong model, Journal of Econometrics, 51, 61-90 (1992) · Zbl 0761.62169
[47] Sethi, R., Endogenous regime switching in speculative markets, Structural Change and Economic Dynamics, 7, 99-118 (1996)
[50] Timmermann, A., How learning in financial markets genetates excess volatility and predictability in stock prices, Quarterly Journal of Economics, 108, 1135-1145 (1993)
[51] Timmermann, A., Excessive volatility and predictability of stock prices in autoregressive dividend models with learning, Review of Economic Studies, 63, 523-557 (1996) · Zbl 0864.90010
[54] Zeeman, E. C., The unstable behavior of stock exchange, Journal of Mathematical Economics, 1, 39-49 (1974) · Zbl 0297.90002
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