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

  • Peter Hammond
  • Yeneng Sun

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