33,598 research outputs found

    Global Stability Conditions on the Plane

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    The paper considers price adjustment on the plane and derives global stability conditions for such dynamics. First, we examine the well-known Scarf Example, to obtain and analyze a global stability condition for this case. Next, for a general class of excess demand functions, a set of conditions is identified which guarantee not only convergence to some equilibrium but also robustness of these properties.

    Market Mood, Adaptive Beliefs and Asset Price Dynamics

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    Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple "dynamic market fraction" model of two groups of traders, fundamentalists and trend followers, under a market maker scenario. Market mood and evolutionary adaption are characterized by fixed and adaptive switching fraction among two groups, respectively. Using local stability and bifurcation analysis, as well as numerical simulation, the role played by the key parameters in the market behaviour is examined. Particular attention is payed to the impact of the market fraction, determined by the fixed proportions of confident fundamentalists and trend followers, and by the proportion of adaptively rational agents, who adopt different strategies over time depending on realized profits.

    Heterogeneity, Market Mechanisms, and Asset Price Dynamics

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    This chapter surveys the boundedly rational heterogeneous agent (BRHA) models of financial markets, to the development of which the authors and several co-authors have contributed in various papers. We give particular emphasis to role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, portfolio implications, the impact of stochastic elements on the markets dynamics, and calibration of this class of models. Due to agents’ behavioural features and market noise, the BRHA models are both nonlinear and stochastic. We show that the BRHA models produce both a locally stable fundamental equilibrium corresponding to that of standard paradigm, as well as instability with a consequent rich range of possible complex behaviours characterised both indirectly by simulation and directly by stochastic bifurcations. A calibrated model is able to reproduce quite well the stylized facts of financial markets. The BRHA framework is thus able to accommodate market features that seem not easily reconcilable for the standard financial market paradigm, such as fat tail, volatility clustering, large excursions from the fundamental and bubbles.Bounded rationality; interacting heterogeneous agents; behavioural finance; nonlinear economic dynamics; complexity

    Double route to chaos in an heterogeneous triopoly game

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    We move from a triopoly game with heterogeneous players (E.M.Elabassy et al., 2009. Analysis of nonlinear triopoly game with heterogeneous players. Computers and Mathematics with Applications 57, 488-499). We remove the nonlinearity from the cost function and introduce it in the demand function. We also introduce a different decisional mechanism for one of the three competitors. A double route to complex dynamics is shown to exist, together with the possibility of multistability of different attractors, requiring a global analysis of the dynamical system.Triopoly game; Heterogeneous players; Global analysis

    Global Stability Conditions on the Plane

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    A Dynamic Analysis of Moving Average Rules

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    The use of various moving average rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules also used in practice. In this paper we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long run) moving average. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag lengths used for the moving averages. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different moving average rules. The price dynamics of the moving average rule is also examined and one of our main findings is that an increase of the window length of the moving average rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.

    The Stochastic Dynamics of Speculative Prices

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    Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.heterogeneous agents; speculative behaviour; random dynamical systems; stochastic bifurcations; invariant measures; chartists
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