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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

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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.

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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. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April. [Downloadable!] (restricted)
  2. 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. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. McCall, John J., 1991. "Exchangeability and its economic applications," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 549-568, July. [Downloadable!] (restricted)
  6. Mordecai Kurz & Martin Schneider, 1996. "Coordination and correlation in Markov rational belief equilibria (*)," Economic Theory, Springer, vol. 8(3), pages 489-520.
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  7. 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. [Downloadable!] (restricted)
  8. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer, vol. 13(3), pages 541-560. [Downloadable!] (restricted)
  9. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March. [Downloadable!]
  10. Carsten Krabbe Nielsen, 1996. "Rational belief structures and rational belief equilibria (*)," Economic Theory, Springer, vol. 8(3), pages 399-422.
  11. Kurz, Mordecai, 1996. "Rational Beliefs and Endogenous Uncertainty," Economic Theory, Springer, vol. 8(3), pages 383-97, October.
  12. 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. [Downloadable!]
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  1. Hanno Lustig, 2001. "The Market Price of Aggregate Risk and the Wealth Distribution," Finance 0111004, EconWPA, revised 16 Nov 2001. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
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