IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i1p131-147.html
   My bibliography  Save this article

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

Author

Listed:
  • Zhu, Mei
  • Wang, Duo
  • Guo, Maozheng

Abstract

We investigate dynamical properties of a heterogeneous agent model with random dividends and further study the relationship between dynamical properties of the random model and those of the corresponding deterministic skeleton, which is obtained by setting the random dividends as their constant mean value. Based on our recent mathematical results, we prove the existence and stability of random fixed points as the perturbation intensity of random dividends is sufficiently small. Furthermore, we prove that the random fixed points converge almost surely to the corresponding fixed points of the deterministic skeleton as the perturbation intensity tends to zero. Moreover, simulations suggest similar behaviors in the case of more complicated attractors. Therefore, the corresponding deterministic skeleton is a good approximation of the random model with sufficiently small random perturbations of dividends. Given that dividends in real markets are generally very low, it is reasonable and significant to some extent to study the effects of heterogeneous agents' behaviors on price fluctuations by the corresponding deterministic skeleton of the random model.

Suggested Citation

  • Zhu, Mei & Wang, Duo & Guo, Maozheng, 2011. "Stochastic equilibria of an asset pricing model with heterogeneous beliefs and random dividends," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 131-147, January.
    • Handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:131-147
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00192-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Potzelberger, Klaus & Sogner, Leopold, 2003. "Stochastic equilibrium: learning by exponential smoothing," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1743-1770, August.
    3. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    4. Hommes, Cars & Huang, Hai & Wang, Duo, 2005. "A robust rational route to randomness in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1043-1072, June.
    5. Medio, Alfredo, 2004. "Invariant Probability Distributions In Economic Models: A General Result," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 162-187, April.
    6. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 95-132, February.
    7. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    8. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233, Elsevier.
    9. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    10. Chiarella, Carl & He, Xue-Zhong, 2003. "Heterogeneous Beliefs, Risk, And Learning In A Simple Asset-Pricing Model With A Market Maker," Macroeconomic Dynamics, Cambridge University Press, vol. 7(4), pages 503-536, September.
    11. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    12. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    13. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    14. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97, January.
    15. Anufriev, Mikhail & Panchenko, Valentyn, 2009. "Asset prices, traders' behavior and market design," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1073-1090, May.
    16. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    17. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    18. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    19. Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2006. "A behavioral asset pricing model with a time-varying second moment," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 535-555.
    20. Dieci, Roberto & Westerhoff, Frank, 2010. "Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 743-764, April.
    21. Kazuo Nishimura & John Stachurski, 2012. "Stability of Stochastic Optimal Growth Models: A New Approach," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 289-307, Springer.
    22. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Carl Chiarella & Roberto Dieci & Xue-Zhong He & Kai Li, 2013. "An evolutionary CAPM under heterogeneous beliefs," Annals of Finance, Springer, vol. 9(2), pages 185-215, May.
    2. Guillaume Coqueret & Bertrand Tavin, 2019. "Procedural rationality, asset heterogeneity and market selection," Post-Print hal-02312310, HAL.
    3. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    4. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.
    5. Coqueret, Guillaume & Tavin, Bertrand, 2019. "Procedural rationality, asset heterogeneity and market selection," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 125-149.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hommes, Cars, 2011. "The heterogeneous expectations hypothesis: Some evidence from the lab," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 1-24, January.
    2. Cars Hommes & Florian Wagener, 2008. "Complex Evolutionary Systems in Behavioral Finance," Tinbergen Institute Discussion Papers 08-054/1, Tinbergen Institute.
    3. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    4. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    5. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.
    7. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    8. Zhu, Mei & Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2009. "Does the market maker stabilize the market?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3164-3180.
    9. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    10. Hommes, Cars & Kiseleva, Tatiana & Kuznetsov, Yuri & Verbic, Miroslav, 2012. "Is More Memory In Evolutionary Selection (De)Stabilizing?," Macroeconomic Dynamics, Cambridge University Press, vol. 16(3), pages 335-357, June.
    11. Cars Hommes, 2010. "The heterogeneous expectations hypothesis: some evidence from the lab," Post-Print hal-00753041, HAL.
    12. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    13. Verbic, Miroslav, 2006. "Memory and Asset Pricing Models with Heterogeneous Beliefs," MPRA Paper 1261, University Library of Munich, Germany.
    14. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    15. Carl Chiarella & Roberto Dieci & Laura Gardini & Lucia Sbragia, 2008. "A Model of Financial Market Dynamics with Heterogeneous Beliefs and State-Dependent Confidence," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 55-72, September.
    16. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2015.
    17. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
    18. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    19. Ming Pu & Gang-Zhi Fan & Seow Ong, 2012. "Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 44(4), pages 543-569, May.
    20. He, Xue-Zhong & Li, Kai, 2012. "Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 973-987.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:131-147. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.