IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i8p2401-2435.html
   My bibliography  Save this article

Limit theorems for individual-based models in economics and finance

Author

Listed:
  • Remenik, Daniel

Abstract

There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions between agents. Our purpose is to present a general framework that encompasses a broad range of models, by proving a law of large numbers and a central limit theorem for certain interacting particle systems with very general state spaces. To do this we draw inspiration from some work done in mathematical ecology and mathematical physics. The first result is proved for the system seen as a measure-valued process, while to prove the second one we will need to introduce a chain of embeddings of some abstract Banach and Hilbert spaces of test functions and prove that the fluctuations converge to the solution of a certain generalized Gaussian stochastic differential equation taking values in the dual of one of these spaces.

Suggested Citation

  • Remenik, Daniel, 2009. "Limit theorems for individual-based models in economics and finance," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2401-2435, August.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2401-2435
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00187-7
    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. Darrell Duffie, 2012. "Over-The-Counter Markets," Introductory Chapters, in: Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets, Princeton University Press.
    2. Steffen Huck & Michael Kosfeld, 2007. "The Dynamics of Neighbourhood Watch and Norm Enforcement," Economic Journal, Royal Economic Society, vol. 117(516), pages 270-286, January.
    3. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    4. Darrell Duffie & Gustavo Manso, 2007. "Information Percolation in Large Markets," American Economic Review, American Economic Association, vol. 97(2), pages 203-209, May.
    5. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    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. Duffie, Darrell & Malamud, Semyon & Manso, Gustavo, 2014. "Information percolation in segmented markets," Journal of Economic Theory, Elsevier, vol. 153(C), pages 1-32.

    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. Duffie, Darrell & Malamud, Semyon & Manso, Gustavo, 2010. "The relative contributions of private information sharing and public information releases to information aggregation," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1574-1601, July.
    2. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    3. Lester, Benjamin & Shourideh, Ali & Venkateswaran, Venky & Zetlin-Jones, Ariel, 2023. "Market-making with search and information frictions," Journal of Economic Theory, Elsevier, vol. 212(C).
    4. Semih Üslü, 2019. "Pricing and Liquidity in Decentralized Asset Markets," Econometrica, Econometric Society, vol. 87(6), pages 2079-2140, November.
    5. Ruiz-Buforn, Alba & Alfarano, Simone & Camacho-Cuena, Eva, 2019. "Price distortions and public information: theory, experiments and simulations," MPRA Paper 93288, University Library of Munich, Germany.
    6. Attanasi, Giuseppe & Centorrino, Samuele & Moscati, Ivan, 2016. "Over-the-counter markets vs. double auctions: A comparative experimental study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 63(C), pages 22-35.
    7. Mikhail Golosov & Guido Lorenzoni & Aleh Tsyvinski, 2014. "Decentralized Trading With Private Information," Econometrica, Econometric Society, vol. 82(3), pages 1055-1091, May.
    8. Charles S. Tapiero, 2015. "A financial CCAPM and economic inequalities," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 521-534, March.
    9. Luigi Iovino, 2012. "Sophisticated Intermediation and Aggregate Volatility," 2012 Meeting Papers 965, Society for Economic Dynamics.
    10. Chague, Fernando & De-Losso, Rodrigo & De Genaro, Alan & Giovannetti, Bruno, 2017. "Well-connected short-sellers pay lower loan fees: A market-wide analysis," Journal of Financial Economics, Elsevier, vol. 123(3), pages 646-670.
    11. Berentsen, Aleksander & Huber, Samuel & Marchesiani, Alessandro, 2016. "The societal benefit of a financial transaction tax," European Economic Review, Elsevier, vol. 89(C), pages 303-323.
    12. Gonzalo Olcina & Vicente Calabuig, 2015. "Coordinated Punishment and the Evolution of Cooperation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(2), pages 147-173, April.
    13. Di Maggio, Marco, 2017. "Comment on: “Dealer balance sheets and bond liquidity provision” by Adrian, Boyarchenko and Shachar," Journal of Monetary Economics, Elsevier, vol. 89(C), pages 110-112.
    14. Steven N. Durlauf, 1996. "Statistical Mechanics Approaches to Socioeconomic Behavior," NBER Technical Working Papers 0203, National Bureau of Economic Research, Inc.
    15. O'Hara, Maureen & Alex Zhou, Xing, 2021. "The electronic evolution of corporate bond dealers," Journal of Financial Economics, Elsevier, vol. 140(2), pages 368-390.
    16. Maryam Farboodi & Gregor Jarosch & Guido Menzio, 2016. "Intermediation as Rent Extraction," PIER Working Paper Archive 16-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2016.
    17. Tomura, Hajime, 2018. "Payment instruments and collateral in the interbank payment system," Journal of Economic Theory, Elsevier, vol. 178(C), pages 82-104.
    18. Arnold Polanski & Emiliya Lazarova, 2015. "Dynamic multilateral markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 815-833, November.
    19. Kiyotaki, Nobuhiro & Lagos, Ricardo & Wright, Randall, 2016. "Introduction to the symposium issue on money and liquidity," Journal of Economic Theory, Elsevier, vol. 164(C), pages 1-9.
    20. Barkley Rosser, J. Jr., 2001. "Complex ecologic-economic dynamics and environmental policy," Ecological Economics, Elsevier, vol. 37(1), pages 23-37, April.

    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:spapps:v:119:y:2009:i:8:p:2401-2435. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.