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Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

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Assets, Beliefs, and Equilibria in Economic Dynamics

Part of the book series: Studies in Economic Theory ((ECON.THEORY,volume 18))

Summary

Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo σ -algebra, which represents macroeconomic risk, individual agents’ random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved.

Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent’s macro workshop at Stanford. We are grateful to him and Felix Kübier in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape.

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Author information

Authors and Affiliations

  1. Department of Economics, Stanford University, Stanford, CA, 94305-6072, USA

    Peter J. Hammond

  2. Institute for Mathematical Sciences, National University of Singapore, 3 Prince George’s Park, Singapore, 118402, Republic of Singapore

    Yeneng Sun

  3. Department of Mathematics and the Centre for Financial Engineering, National University of Singapore, Singapore, Republic of Singapore

    Yeneng Sun

Authors
  1. Peter J. Hammond
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  2. Yeneng Sun
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Corresponding author

Correspondence to Peter J. Hammond .

Editor information

Editors and Affiliations

  1. Department of Economics, Krannert School of Management, Purdue University, Rawls Hall, West Lafayette, IN, 47907-2076, USA

    Charalambos D. Aliprantis

  2. Department of Economics, Stanford University, Stanford, CA, 94305-6072, USA

    Kenneth J. Arrow , Peter Hammond  & Felix Kubler ,  & 

  3. Department of International Business, National Taiwan University, Taipei, Taiwan R.O.C.

    Ho-Mou Wu

  4. Department of Economics, University of Illinois, 330 Commerce West Building, Champaign, IL, 61820, USA

    Nicholas C. Yannelis

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© 2004 Springer-Verlag Berlin Heidelberg

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Hammond, P.J., Sun, Y. (2004). Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case. In: Aliprantis, C.D., Arrow, K.J., Hammond, P., Kubler, F., Wu, HM., Yannelis, N.C. (eds) Assets, Beliefs, and Equilibria in Economic Dynamics. Studies in Economic Theory, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05858-9_34

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  • DOI: https://doi.org/10.1007/978-3-662-05858-9_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05663-5

  • Online ISBN: 978-3-662-05858-9

  • eBook Packages: Springer Book Archive

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