Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends

Zhu, Meiling; Wang, Duo; Guo, Maozheng

doi:10.1016/j.jedc.2010.09.003

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…For example, in [10] the original random model is studied by using an approximate deterministic model which is given by setting the random dividend in the random model as a constant, its mean. With the theorem and propositions in this paper, it can be proved that there exists a unique stable stationary solution in a small neighborhood of the fixed point of the corresponding deterministic difference equation provided the perturbation intensity is sufficiently small (see [16]). Thus from the dynamic point of view, the dynamic properties are very close for the random model and the corresponding deterministic model near the fixed point since random dividends in real markets are generally small.…”

Section: Discussionmentioning

confidence: 96%

See 1 more Smart Citation

Existence and stability of stationary solutions of nonlinear difference equations under random perturbations

Zhu

Wang

Guo

2010

Journal of Difference Equations and Applications

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Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. AbstractExistence and stability of stationary solutions of nonlinear random difference equations are studied in this note. Firstly, we give the weak conditions that guarantee the stability of Lypanunov exponents under small random perturbations. Secondly, we find out the conditions under which the ratio of the random norm and the standard Euclidean norm has deterministic bounds. Based on these new results, we provide easy-to-use conditions that guarantee the existence and almost sure stability of a stationary solution. In addition, we also prove that the stationary solution converges with probability one to the fixed point of the corresponding deterministic system as the noise intensity tends to zero.

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Section: Discussionmentioning

confidence: 96%

“…In fact, Young [14] studied a more general case. However, some practical models (see [16]) do not satisfy the conditions given by [14]. In order to deal with the special cases related to the practical models, we provide some weaker conditions than those given by [14].…”

Section: Introductionmentioning

confidence: 99%

Existence and stability of stationary solutions of nonlinear difference equations under random perturbations

Zhu

Wang

Guo

2010

Journal of Difference Equations and Applications

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“…The usual argument is that if the randomness is modest, then the system is only marginally perturbed and converges to the fixed-state described in the deterministic case. In different contexts, Benaïm and Weibull (2003) and Zhu et al (2011b) show that stochastic systems asymptotically converge to the deterministic equilibria when the noise is sufficiently small. Below, we formally discuss this assertion for our model in more detail.…”

Section: Random Dividend Yieldsmentioning

confidence: 99%

“…The literature provides results in this direction. In Zhu et al (2011b), the authors investigate the relationship between the deterministic skeleton of an heterogeneous agent model and its stochastic counterpart, namely when noise is added to the dividend process. To do so they rely on results obtained in Zhu et al (2011a).…”

Section: Introductionmentioning

confidence: 99%

Procedural Rationality, Asset Heterogeneity and Market Selection

Coqueret

Tavin

2017

SSRN Journal

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We extend the agent-based model of Anufriev and Bottazzi (2010) to the case with many risky assets. We show that under the procedural equilibrium, all assets with nonzero aggregate demand must have the same price returns. Heterogeneity in price returns appears when some assets face zero demand. In this case, the returns are essentially driven by the matrix of wealth-weighted products between demands and they generate a rich variety of patterns for agents' market shares. We formalize the dynamics of deterministic skeletons in our market model and consider the associated Jacobian matrix, for which we provide a closed form expression up to a matrix inversion. We then introduce the characteristic ratio of an investment strategy, which involves the average dividend yields of the risky assets and the investors' portfolio compositions. When equilibrium returns are uniform and when the number of assets is not smaller than the number of agents, the equilibrium with a single survivor can only be stable if the survivor has the maximal characteristic ratio. Moreover, we prove that this stability criterion holds as long as the noise in the system is sufficiently small. We confirm all our findings with a thorough empirical analysis of numerical simulations, with and without noise. All in all, our results form a theoretical rationale for portfolio strategies tilted towards firms that pay high dividend yields.

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An evolutionary CAPM under heterogeneous beliefs

Chiarella

Dieci

et al. 2012

Ann Finance

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We would like to thank Cars Hommes for a stimulating discussion in the early stages of this project. We are grateful to valuable comments from two anonymous referees. Dieci gratefully acknowledges a Visiting Professor Appointment at the Quantitative Finance Research Centre, UTS Business School, during which this work was finalised. Dieci also acknowledges support from MIUR under project PRIN 2009 "Local interactions and global dynamics in economics and finance: models and tools" and from EU COST within Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation". Financial support for Chiarella and He from the Australian Research Council (ARC) under Discovery Grant (DP110104487) is gratefully acknowledged.

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Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends

Cited by 6 publications

References 32 publications

Existence and stability of stationary solutions of nonlinear difference equations under random perturbations

Existence and stability of stationary solutions of nonlinear difference equations under random perturbations

Procedural Rationality, Asset Heterogeneity and Market Selection

An evolutionary CAPM under heterogeneous beliefs

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