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Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The Symmetric Case

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  • Peter Hammond
  • Yeneng Sun

Abstract

October 2001 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 sigma-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. Working Papers Index

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 01015.

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Date of creation: Oct 2001
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Handle: RePEc:wop:stanec:01015

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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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  3. Carsten Krabbe Nielsen, 1996. "Rational belief structures and rational belief equilibria (*)," Economic Theory, Springer, vol. 8(3), pages 399-422.
  4. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560.
  5. Kutz, M. & Schneider, M., 1996. "Coordination and Correlation in Markov Rational Belief Equilibria," Papers 281, Banca Italia - Servizio di Studi.
  6. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April.
  7. Kurz, Mordecai, 1996. "Rational Beliefs and Endogenous Uncertainty," Economic Theory, Springer, vol. 8(3), pages 383-97, October.
  8. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
  9. Kohlberg, Elon & Reny, Philip J., 1997. "Independence on Relative Probability Spaces and Consistent Assessments in Game Trees," Journal of Economic Theory, Elsevier, vol. 75(2), pages 280-313, August.
  10. Peter J. Hammond & Yeneng Sun, 2000. "Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables," Working Papers 00008, Stanford University, Department of Economics.
  11. McCall, John J., 1991. "Exchangeability and its economic applications," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 549-568, July.
  12. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
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Cited by:
  1. YiLi Chien & Hanno Lustig, 2010. "The Market Price of Aggregate Risk and the Wealth Distribution," Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1596-1650, April.
  2. 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.
  3. 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.
  4. 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.
  5. Kr├╝ger, 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.
  6. 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.
  7. 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.
  8. 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.

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