Papers by Mikhail Anufriev
In this paper we explore how specific aspects of market transparency and agents behavior affect t... more In this paper we explore how specific aspects of market transparency and agents behavior affect the efficiency of the market outcome. In particular, we are interested whether learning behavior with and without information about actions of other participants improves market efficiency. We consider a simple market for a homogeneous good populated by buyers and sellers. The valuations of the buyers and the costs of the sellers are given exogenously. Agents are involved in the consecutive trading sessions, which are organized as a continuous double auction with electronic book. Using Individual Evolutionary Learning mechanism agents submit price bids and offers, trying to learn the most profitable strategy by looking at their realized and counterfactual or "foregone" payoffs. We find that learning outcomes heavily depend on information treatments. Under full information agents' orders tend to be similar, while under limited information agents submit their valuations/costs. This results in higher price volatility for the latter treatment. We also find that learning improves allocative efficiency when compared with the outcomes with Zero-Intelligence traders.
Journal of Economic Dynamics & Control, 2009
The dynamics of a financial market with heterogeneous agents are analyzed under different market ... more The dynamics of a financial market with heterogeneous agents are analyzed under different market architectures. We start with a tractable behavioral model under Walrasian market clearing and simulate it under different trading protocols. The key behavioral feature of the model is the switching by agents between simple forecasting rules on the basis of a fitness measure. By analyzing the dynamics under order-driven protocols we show that the behavioral and structural assumptions of the model are closely intertwined. * An earlier version of this paper was prepared while Mikhail Anufriev was visiting UNSW, whose hospitality he gratefully acknowledges. We wish to thank all the participants of the Symposium on Agent-Based Computational Methods in Economics and Finance in Aalborg, of the Workshop on "Complexity in Economics and Finance" in Leiden, and of the seminars in Amsterdam, Pisa, Sydney, and Trieste for useful comments and stimulating questions. We especially thank Giulio Bottazzi, Buz Brock, Cars Hommes, and Florian Wagener for providing very detailed comments during different stages of the work. We also thank the editor and two anonymous referees.
Current Medical Research and Opinion, 2010
In this paper we explore how specific aspects of market transparency and agents’ behavior affect ... more In this paper we explore how specific aspects of market transparency and agents’ behavior affect the efficiency of the market outcome. In particular, we are interested whether learning behavior with and without information about actions of other participants improves market efficiency. We consider a simple market for a homogeneous good populated by buyers and sellers. The valuations of the buyers and the costs of the sellers are given exogenously. Agents are involved in consecutive trading sessions, which are organized as a continuous double auction with order book. Using Individual Evolutionary Learning agents submit price bids and offers, trying to learn the most profitable strategy by looking at their realized and counterfactual or “foregone” payoffs. We find that learning outcomes heavily depend on information treatments. Under full information about actions of others, agents’ orders tend to be similar, while under limited information agents tend to submit their valuations/costs. This behavioral outcome results in higher price volatility for the latter treatment. We also find that learning improves allocative efficiency when compared to outcomes with Zero-Intelligent traders.
The paper analyzes the dynamics in a model with heterogeneous agents trading in simple markets un... more The paper analyzes the dynamics in a model with heterogeneous agents trading in simple markets under different trading protocols. Starting with the analytically tractable model of [4], we build a simulation platform with the aim to investigate the impact of the trading rules on the agents’ ecology and aggregate time series properties. The key behavioral feature of the model is the presence of a finite set of simple beliefs which agents choose each time step according to a fitness measure. The price is determined endogenously and our focus is on the role of the structural assumption about the market architecture. Analyzing dynamics under such different trading protocols as the Walrasian auction, the batch auction and the ‘order-book’ mechanism, we find that the resulting time series are similar to those originating from the noisy version of the model [4]. We distinguish the randomness caused by a finite number of agents and the randomness induced by an order-based mechanisms and analyze their impact on the model dynamics.
Journal of Economic Behavior & Organization, 2009
High degrees of relative risk aversion induce indeterminacy in cashin-advance economies. This pap... more High degrees of relative risk aversion induce indeterminacy in cashin-advance economies. This paper Þnds that Taylor-style policies can pre-empt such sunspot equilibria. SpeciÞc policy recommendations depend on the fundamentals of the economy, i.e. the empirically true value of coefficient of relative risk aversion. * This paper was written while I was a DFG Heisenberg Fellow. I would like to thank the Federal Reserve Bank of San Francisco for its hospitality as well as Chuck Carlstrom and one anonymous referee for helpful comments.
Evolutionary Switching between Forecasting Heuristics: An Explanation of an Asset-Pricing Experiment
In this paper we propose an explanation of the findings of a recent laboratory market forecasting... more In this paper we propose an explanation of the findings of a recent laboratory market forecasting experiment. In the experiment the participants were asked to predict prices for 50 periods on the basis of past realizations. Three different aggregate outcomes were observed in an identical environment: slow monotonic price convergence, persistent price oscillations, and oscillatory dampened price fluctuations. Individual predictions exhibited a high degree of coordination, although the individual forecasts were not commonly known. To explain these findings we propose an evolutionary model of reinforcement learning over a set of simple forecasting heuristics. The key element of our model is the switching between heuristics on the basis of their past performance. Simulations show that such evolutionary learning can reproduce the qualitative patterns observed in the experiment.
We consider a simple pure exchange economy with two assets, one riskless, yielding a constant ret... more We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return on investment, and one risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed through the market clearing condition. Individual demands are expressed as fractions of traders wealth and depend on traders forecasts about future price movement. Under these assumptions, we derive the stochastic dynamical system that describes the evolution of price and wealth. We study the cases in which one or two agents operate in the market, identifying the possible equilibria and discussing their stability conditions. The main novelty of this paper rests in the abstraction from the precise characterization of agents' beliefs and preferences. In this respect our results generalize several previous contributions in the field. In particular, we show that, irrespectively of agents' behavior, the system can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where heterogeneous agents hold finite shares of the aggregate wealth. Moreover, we show that all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the role of different parameters for the stability of equilibria and the selection principle governing market dynamics.
Journal of Economic Behavior & Organization, 2009
In recent 'learning to forecast' experiments with human subjects , three different patterns in ag... more In recent 'learning to forecast' experiments with human subjects , three different patterns in aggregate asset price behavior have been observed: slow monotonic convergence, permanent oscillations and dampened fluctuations. We construct a simple model of individual learning, based on performance based evolutionary selection or reinforcement learning among heterogeneous expectations rules, explaining these different aggregate outcomes. Out-of-sample predictive power of our switching model is higher compared to the rational or other homogeneous expectations benchmarks. Our results show that heterogeneity in expectations is crucial to describe individual forecasting behavior as well as aggregate price behavior.
Knowledge Engineering Review, 2007
The time evolution of aggregate economic variables, such as stock prices, is affected by market e... more The time evolution of aggregate economic variables, such as stock prices, is affected by market expectations of individual investors. Neo-classical economic theory assumes that individuals form expectations rationally, thus enforcing prices to track economic fundamentals and leading to an efficient allocation of resources. However, laboratory experiments with human subjects have shown that individuals do not behave fully rational but instead follow simple heuristics. In laboratory markets prices may show persistent deviations from fundamentals similar to the large swings observed in real stock prices.
We consider a simple pure exchange economy with two assets: one riskless, yielding a constant ret... more We consider a simple pure exchange economy with two assets: one riskless, yielding a constant return on investment, and the other risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed by imposing a market clearing condition on the sum of individual demand functions. Individual demand for the risky asset is expressed as a fraction of wealth and depends on how traders forecast future price movement. Under these assumptions we derive the stochastic dynamical system describing the evolution of price and wealth.
Current Medical Research and Opinion, 2010
An economic environment is a feedback system, where dynamics of aggregate variables depend on ind... more An economic environment is a feedback system, where dynamics of aggregate variables depend on individual expectations and also shape them. The type of feedback mechanism is crucial for the aggregate outcome. Experiments with human subjects (Heemeijer, Hommes, Sonnemans, and Tuinstra, 2009) have shown that price converges to the fundamental level in the negative feedback environment but fails to do so under positive feedback. We present an explanation of these experimental results by means of a model of evolutionary switching between heuristics. Active heuristics are chosen endogenously, on the basis of their past performance. Under negative feedback an adaptive heuristic dominates explaining fast price convergence, whereas under positive feedback a trend-following heuristic dominates resulting in persistent price deviations and oscillations.
We consider a simple pure exchange economy with two assets, one riskless, yielding a constant ret... more We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return on investment, and one risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed by imposing market clearing condition on the sum of traders individual demand functions. We assume that agents' strategies are consistent with maximizing a CRRA utility, so that the individual demand for the risky asset is expressed as a fraction of the agent's wealth and the evolution of price and wealth distribution is described by means of a dynamical system. We consider agents whose individual demand function is based on future prices forecasts obtained on the basis of past market history and we analyze two cases.
Journal of Economic Dynamics & Control, 2006
We consider a simple pure exchange economy with two assets: one riskless, yielding a constant ret... more We consider a simple pure exchange economy with two assets: one riskless, yielding a constant return on investment, and the other risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed by imposing a market clearing condition on the sum of individual demand functions. Individual demand for the risky asset is expressed as a fraction of wealth and depends on how traders forecast future price movement. Under these assumptions we derive the stochastic dynamical system describing the evolution of price and wealth.
In recent 'learning to forecast' experiments with human subjects (Hommes, et al. 2005), three dif... more In recent 'learning to forecast' experiments with human subjects (Hommes, et al. 2005), three different patterns in aggregate price behavior have been observed: slow monotonic convergence, permanent oscillations and dampened fluctuations. We
The presence of excess covariance in financial price returns is an accepted empirical fact: the p... more The presence of excess covariance in financial price returns is an accepted empirical fact: the price dynamics of financial assets tend to be more correlated than their fundamentals would justify. We propose an intertemporal equilibrium multi-assets model of financial markets with an explicit and endogenous price dynamics. The market is driven by an exogenous stochastic process of dividend yields paid by the assets that we identify as market fundamentals. The model is rather flexible and allows for the coexistence of different trading strategies. The evolution of assets price and traders' wealth is described by a high-dimensional stochastic dynamical system. We identify the equilibria of the model consistent with a baseline assumption of procedural rationality. We show that these equilibria are characterized by excess covariance in prices with respect to the dividend process. Moreover, we show that in equilibrium there is a positive expected marginal profit in choosing more risky portfolios. As a consequence, the evolutionary pressure generates a trend towards more remunerative strategies, which, in turn, increase the variance of prices and the dynamic instability of the system. JEL classification codes: D81, G11, G12
Journal of Economic Behavior & Organization, 2009
We analyze the endogenous price formation mechanism of a pure exchange economy with two assets, r... more We analyze the endogenous price formation mechanism of a pure exchange economy with two assets, riskless and risky. The economy is populated by an arbitrarily large number of traders whose investment choices are described by means of generic smooth functions of past realizations. These choices can be consistent with (but not limited to) the solutions of expected utility maximization problems.
Journal of Mathematical Economics, 2010
We analyze the endogenous price formation mechanism of a pure exchange economy with two assets, r... more We analyze the endogenous price formation mechanism of a pure exchange economy with two assets, riskless and risky. The economy is populated by an arbitrarily large number of traders whose investment choices are described by means of generic smooth functions of past realizations. These choices can be consistent with (but not limited to) the solutions of expected utility maximization problems.
This paper analyzes to what extent and how the trading activity of a group of heterogeneous agent... more This paper analyzes to what extent and how the trading activity of a group of heterogeneous agents can be described, in the aggregate, as the result of the investment decision of a single “representative” agent. We consider a two-asset pure exchange economy populated by CRRA traders whose individual demands are functions of the past market history. If individual choices are expressed as noisy versions of a common behavior, and the number of agents is large, one can consider the Large Market Limit of the economy and reduce the model to a low-dimensional stochastic system. We investigate the goodness of this approximation under different market conditions and different agents ecologies. The results of the analysis can be used in the study of the general case with an arbitrary number of heterogeneous agents.
We study the co-evolution of asset prices and individual wealth in a financial market populated b... more We study the co-evolution of asset prices and individual wealth in a financial market populated by an arbitrary number of heterogeneous, boundedly rational agents. Using wealth dynamics as a selection device we are able to characterize the long run market outcomes, i.e. asset returns and wealth distributions, for a general class of investment behaviors. Our investigation illustrates that market interaction and wealth dynamics pose certain limits on the outcome of agents' interactions even within the "wilderness of bounded rationality". As an application we consider the case of heterogeneous meanvariance optimizers and provide insights into the results of the simulation model introduced by Levy, Levy and Solomon (1994).
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Papers by Mikhail Anufriev