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Equilibria in Financial Markets with Heterogeneous Agents: A New Perspective
Abstract:
We analyse models in which agents on financial markets form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are “chartist” or extrapolatory rules. When these predominate prices can exhibit transient behaviour. However, we give conditions under which the limit distribution of the price process exists and is unique.This limit distribution may be thought of as the appropriate equilibrium notion for such markets. If the probability that an agent will switch to being a “chartist” is not too high then the process does not explode. Thus there are occasional bubbles but they inevitably burst. The distribution reflects the presence of chartists since it exhibits fatter tails than the normal distribution. A number of characteristics of financial time series are captured by this sort of model.
Hans Föllmer, Ulrich Horst, and Alan Kirman
25th February 2004
Market Selection when Markets are Incomplete
Abstract:
Consider a two period exchange economy with dividend uncertainty. Agents have different beliefs, endowments and utility functions. This results in different motives for trading, such as risk-sharing and speculation. In the first period agents trade Arrow securities in zero supply. The set of available Arrow securities is of a specific form, but it can be complete or incomplete. In the second period one out of many possible states of nature is realized. I show that agents with more accurate beliefs (in the sense of higher market entropy) will accumulate more wealth and therefore dominate the economy. This holds regardless of agents’ preferences over risk and in both complete and incomplete market economies. These results indicate that belief accuracy rather than preferences over risk is the critical factor determining survival. However, the exact sense in which agents with more accurate beliefs become wealthier is stronger in complete market economies than in incomplete market economies.
Alvaro Sandroni
February 16, 2004
The Asset Market Game
Abstract:
This paper models asset markets as a game where assets pay according to an arbitrary returns matrix, investors decide on fractions of wealth to allocate to each asset, and prices result from market clearing. The only pure strategy Nash equilibrium is to split wealth proportionally to the assets’ expected returns, which can be interpreted as investing according to the fundamentals. Further, the equilibrium strategy is evolutionarily stable in the sense of Schaffer (1988). We also study the stability properties of the equilibrium in an evolutionary dynamics where wealth flows with higher probability into those strategies that obtain higher realized payoffs.
Carlos Alós-Ferrer, Ana B. Ania
January 2004
Institutional Architectures and Behavioral Ecologies in the Dynamics of Financial Markets
Abstract:
The paper examines the properties of nancial market dynamics, under different trading protocols. We start with an empirical analysis of the statistical properties of daily data from the world's major Stock Exchanges, comparing the behavior of different market phases characterized by different trading protocols. The evidence lends support to the importance of investigating the outcome of alternative market mechanisms. Motivated by this nding, we present an agent-based model allowing the consistent treatment of agents' behavior under three different trading set-ups, namely a Walrasian auction, a batch auction and an `order-book' mechanism. The results highlight the importance of the institutional setting in shaping the dynamics of the market but also suggest that the latter can become the outcome of a complicated interaction between the trading protocol and the ecology of traders behaviors. In particular, we show that market architectures bear a central in uence upon the time series properties of market dynamics. Conversely, the revealed allocative effciency of different market settings is strongly influenced by the
trading behavior of agents.
Giulio Bottazzi Giovanni Dosi Igor Rebesco
December 31, 2003
Market Selection and Survival of Investment Strategies
Abstract:
The paper analyzes the process of market selection of investment strategies in an incomplete market of short-lived assets. In the model under study, asset payoffs depend on exogenous random factors. Market participants use dynamic investment strategies taking account of the available information about current and previous events. It is shown that an investor allocating wealth across the assets according to their conditional expected payoffs eventually accumulates total market wealth, provided the investor’s strategy is asymptotically distinct from the portfolio rule suggested by the Capital Asset Pricing Model. This assumption turns out to be essentially necessary for the result.
Rabah Amira, Igor V. Evstigneev, Thorsten Hens and Klaus Reiner Schenk–Hoppé
October 27, 2003
Evolutionary dynamics in markets with many trader types
Abstract:
This paper develops the notion of a Large Type Limit (LTL) describing the dynamical behavior of heterogeneous markets with many trader types. It is shown that generic and persistent features of adaptive evolutionary systems with many trader types are well described by the large type limit. Stability and bifurcation routes to instability and strange attractors in a simple evolutionary financial market model are studied. An increase in the "intensity of adaptation" or in the diversity of beliefs may lead to deviations from an unstable RE fundamental benchmark and excess volatility. A large evolutionary system may thus become unstable and complicated dynamics may arise when agents become sensitive to small differences in fitness.
William A. Brock, Cars H. Hommes, Florian O. O. Wagner
July 10, 2003
Evolutionary Stability of Portfolio Rules in Incomplete Markets
Abstract:
This paper studies the evolution of wealth shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of repeated reinvestment of wealth is determined by the wealth share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and suffcient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean-variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.
Thorsten Hens, Klaus Reiner Schenk-Hoppé
April 16, 2003
Is Risk-Aversion Hereditary?
Abstract:
The degree of risk-aversion determines portfolio holdings and subsequently the distribution of wealth. Do we inherit our preferences, or are they determined randomly or through experience? Can preferences be “learned”? The empirically observed Pareto wealth distribution at the high-wealth range may provide an answer to these questions. We show that the Pareto wealth distribution implies an upper bound on the role of heredity in determining risk-aversion.
Moshe Levy
First version: September 2002
Genetic Learning as an Explanation of Stylized Facts of Foreign Exchange Markets
Abstract:
This paper revisits the Kareken-Wallace model of exchange rate formation in a two country overlapping generations world. Following the seminal paper by Arifovic (Journal of Political Economy, 104, 1996, 510 – 541) we investigate a dynamic version of the model in which agents’ decision rules are updated using genetic algorithms. Our main interest is in whether the equilibrium dynamics resulting from this learning process helps to explain the main stylized facts of free-floating exchange rates (unit roots in levels together with fat tails in returns and volatility clustering). Our time series analysis of simulated data indicates that for particular parameterizations, the characteristics of the exchange rate dynamics are, in fact, very similar to those of empirical data. The similarity appears to be quite insensitive with respect to some of the ingredients of the genetic algorithm (i.e. utility-based versus rankbased or tournament selection, binary or real coding). However, appearance or not of realistic time series characteristics depends crucially on the mutation probability (which should be low) and the number of agents (not more than about 1000). With a larger population, this collective learning dynamics looses its realistic appearance and instead exhibits regular periodic oscillations of the agents’ choice variables.
Thomas Lux, Sascha Schornstein
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