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

## Author Info

• Peter J. Hammond
• Yeneng Sun
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## Abstract

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 -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. Copyright Springer-Verlag Berlin Heidelberg 2003

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## Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 21 (2003)
Issue (Month): 2 (03)
Pages: 743-766

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Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:743-766

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## Related research

Keywords: Keywords and Phrases: Large economy; Continuum of agents; Law of large numbers; Exchangeability; Joint measurability problem; de Finetti's theorem; Monte Carlo convergence; Monte Carlo $\sigma$-algebra.; JEL Classification Numbers: D80; C00; E00.;

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• JEL - Labor and Demographic Economics - - - - -
• Cla - Mathematical and Quantitative Methods - - - - -
• Num - Economic History - - - - -

## References

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1. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
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5. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560.
6. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April.
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10. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
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## Citations

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Cited by:
1. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Core, equilibria and incentives in large asymmetric information economies," Games and Economic Behavior, Elsevier, vol. 61(1), pages 131-155, October.
2. Hammond, Peter J. & Sun, Yeneng, 2007. "Monte Carlo Simulation of Macroeconomic Risk with a Continuum Agents : The General Case," The Warwick Economics Research Paper Series (TWERPS) 803, University of Warwick, Department of Economics.
3. Hanno Lustig, 2001. "The Market Price of Aggregate Risk and the Wealth Distribution," Finance 0111004, EconWPA, revised 16 Nov 2001.
4. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer, vol. 36(2), pages 303-325, August.
5. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.
6. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
7. Dirk Krueger & Hanno Lustig, 2006. "When is Market Incompleteness Irrelevant for the Price of Aggregate Risk (and when is it not)?," NBER Working Papers 12634, National Bureau of Economic Research, Inc.
8. Krüger, Dirk & Lustig, Hanno, 2006. "The Irrelevance of Market Incompleteness for the Price of Aggregate Risk," CEPR Discussion Papers 5936, C.E.P.R. Discussion Papers.

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