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Limit theorems for individual-based models in economics and finance

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  • Remenik, Daniel
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 119 (2009)
    Issue (Month): 8 (August)
    Pages: 2401-2435

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    Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2401-2435

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    Keywords: Individual-based model Interacting particle system Law of large numbers Central limit theorem Fluctuation process Measure-valued process Finance Economics;

    References

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    1. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    2. Mark H. A. Davis & Juan Carlos Esparragoza-Rodriguez, 2007. "Large Portfolio Credit Risk Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 653-678.
    3. Darrell Duffie & Gustavo Manso, 2007. "Information Percolation in Large Markets," American Economic Review, American Economic Association, vol. 97(2), pages 203-209, May.
    4. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2004. "Over-the-Counter Markets," NBER Working Papers 10816, National Bureau of Economic Research, Inc.
    5. Steffen Huck & Michael Kosfeld, . "The Dynamics of Neighbourhood Watch and Norm Enforcement," IEW - Working Papers 199, Institute for Empirical Research in Economics - University of Zurich.
    6. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
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