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13
Overconfidence and speculative bubbles
 Journal of Political Economy
, 2003
"... Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an ass ..."
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Cited by 136 (11 self)
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Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an asset owner has an option to sell the asset to other overconfident agents when they have more optimistic beliefs. As in Harrison and Kreps (1978), this resale option has a recursive structure, that is, a buyer of the asset gets the option to resell it. Agents pay prices that exceed their own valuation of future dividends because they believe that in the future they will find a buyer willing to pay even more. This causes a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. In equilibrium, large bubbles are accompanied by large trading volume and high price volatility. Our model has an explicit solution, which allows for several comparative statics exercises. Our analysis shows that while Tobin’s tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility. We also give an example where the price of a subsidiary is larger than its parent firm. This paper was previously circulated under the title “Overconfidence, ShortSale Constraints and Bubbles.”
A limit theorem for financial markets with inert investors
 Mathematics of Operations Research
, 2003
"... We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semiMarkov processes are tailor made for modeling inert investors. With a suitable scaling, we show that when t ..."
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Cited by 16 (2 self)
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We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semiMarkov processes are tailor made for modeling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process with long range dependence and nonGaussian returns distributions, driven by a fractional Brownian motion. Consequently, investor inertia may lead to arbitrage opportunities for sophisticated ‘third parties’. The mathematical contributions are a functional central limit theorem for stationary semiMarkov processes, and approximation results for stochastic integrals of continuous semimartingales with respect to fractional Brownian motion.
Equilibria in systems of social interactions
, 2003
"... Although models of social interactions have been used extensively to explain a myriad of economic and social phenomena, there are few general theorems concerning the existence, uniqueness or the limit behavior of equilibria in the literature. In this paper we consider systems with local and global s ..."
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Cited by 9 (0 self)
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Although models of social interactions have been used extensively to explain a myriad of economic and social phenomena, there are few general theorems concerning the existence, uniqueness or the limit behavior of equilibria in the literature. In this paper we consider systems with local and global social interactions. Individuals’ utilities depend on the actual choices made by their “neighbors, ” and on the empirical distribution of actions throughout the population. We discuss conditions that insure existence or uniqueness of equilibria. These conditions impose bounds on the amount of social influence on an agent’s decision. We also establish limit results as the systems become large.
Overconfidence, ShortSale Constraints, and Bubbles
 JOURNAL OF POLITICAL ECONOMY
, 2001
"... Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to othe ..."
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Cited by 5 (0 self)
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Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to other agents when they have more optimistic beliefs. This resale option has a recursive structure, that is a buyer of the asset gets the option to resell it, causing a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. The model generates prices that are above fundamentals, excessive trading, and excess volatility. We also give an example where the price of a subsidiary is larger than its parent firm. Our analysis shows that while Tobin's tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility.
Stochastic Games with Infinitely many Interacting Agents
"... We introduce and study a class of infinitehorizon nonzerosum noncooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminat ..."
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Cited by 2 (1 self)
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We introduce and study a class of infinitehorizon nonzerosum noncooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.
Queueing Theoretic Approaches to Financial Price Fluctuations ∗
, 2006
"... One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate. This agentbased viewpoint in finance goes back at least to t ..."
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Cited by 1 (0 self)
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One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate. This agentbased viewpoint in finance goes back at least to the work of Garman (1976) and shares the philosophy of statistical mechanics in the physical sciences. We discuss recent developments in market microstructure models. They are capable, often through numerical simulations, to explain many stylized facts like the emergence of herding behavior, volatility clustering and fat tailed returns distributions. They are typically queueingtype models, that is, models of order flows, in contrast to classical economic equilibrium theories of utilitymaximizing, rational, “representative ” investors. Mathematically, they are analyzed using tools of functional central limit theorems, strong approximations and weak convergence. Our main examples focus on investor inertia, a trait that is welldocumented, among other behavioral qualities, and modelled using semiMarkov switching processes. In particular, we show how inertia may lead to the phenomenon of longrange dependence in stock
Queuing, social interactions, and the . . .
, 2006
"... We consider an agentbased model of financial markets with asynchronous order arrival in continuous time. Buying and seeling orders arrive in accordance with a Poisson dynamics where the order rates depend both on past prices and the mood of the market. The agents form their demand for an asset on t ..."
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We consider an agentbased model of financial markets with asynchronous order arrival in continuous time. Buying and seeling orders arrive in accordance with a Poisson dynamics where the order rates depend both on past prices and the mood of the market. The agents 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. Among the possible rules are “chartist ” or extrapolatory rules. We prove that when chartists are in the market, and with choice of scaling, the dynamics of asset prices can be approximated by an ordinary delay differential equation. The fluctuations around the first order approximation follow an OrnsteinUhlenbeck dynamics with delay in a random environment of investor sentiment.
MULTIAGENT MODELS IN TIMEVARYING AND RANDOM ENVIRONMENT
, 2006
"... In this paper we study multiagent models with timevarying type change. Assume that there exist a closed system of N agents classified into r types according to their states of an internal system; each agent changes its type by an internal dynamics of the internal states or by the relative frequency ..."
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In this paper we study multiagent models with timevarying type change. Assume that there exist a closed system of N agents classified into r types according to their states of an internal system; each agent changes its type by an internal dynamics of the internal states or by the relative frequency of different internal states among the others, e.g., multinomial sampling. We investigate the asymptotic behavior of the empirical distributions of the agents ’ types as N goes to infinity, by the weak convergence criteria for timeinhomogeneous Markov processes and the theory of Volterra integral equations of the second kind. We also prove convergence theorems of these models evolving in random environment.
Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
, 2012
"... Stochastic partial differential equations (SPDEs) whose solutions are probabilitymeasurevalued processes are considered. Measurevalued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particu ..."
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Stochastic partial differential equations (SPDEs) whose solutions are probabilitymeasurevalued processes are considered. Measurevalued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation, and the infinite system of SDEs, assumed to be exchangeable, is coupled through a common noise process and through the asset prices. In the simplest, single asset setting, the market clearing price at any time t is given by a quantile of the de Finetti measure determined by the individual trader valuations. In the multiasset setting, the prices are essentially given by the solution of an assignment game introduced by Shapley and Shubik. Existence of solutions for the infinite exchangeable system is obtained by an approximation argument that requires the continuous dependence of the prices on the determining de Finetti measures which is ensured if the de Finetti measures charge every open set.
Perfect Forecasting, Behavioral Heterogeneities, and Asset Prices ∗
, 2008
"... This survey reviews a dynamic multiasset framework in which heterogeneous agents with multiperiod planning horizons interact. This framework distinguishes between temporary equilibrium maps describing the basic market mechanism of an asset market, forecasting rules which model the way in which exp ..."
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This survey reviews a dynamic multiasset framework in which heterogeneous agents with multiperiod planning horizons interact. This framework distinguishes between temporary equilibrium maps describing the basic market mechanism of an asset market, forecasting rules which model the way in which expectations are formed, and a model for exogenous random perturbations. Perfect forecasting rules which provide correct forecasts for first and second moments of future prices are introduced. Based on these perfect forecasting rules, fundamental concepts of the traditional CAPM are extended to a setting in which beliefs are not homogeneous. We review a multifund separation theorem and introduce the notion of a generational portfolio which is held by investors with homogeneous beliefs and identical planning horizons. It is shown that social interaction among consumers may endogenously create risk leading to nonergodic behavior of asset prices. The stochastic dynamics of asset prices, beliefs, portfolio holdings, and market shares are illustrated with numerical simulations. ∗ Acknowledgment. This work is a survey prepared for a chapter in the forthcoming Handbook of Finance, edited by Klaus Reiner SchenkHoppé and Thorsten Hens. I would like