Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case |
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| Authors: | Peter J Hammond Yeneng Sun |
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| Institution: | (1) Department of Economics, Stanford University, Stanford, CA 94305-6072, USA (e-mail: peter.hammond@stanford.edu) , US;(2) Institute for Mathematical Sciences, National University of Singapore, 3 Prince George's Park, Singapore 118402, REPUBLIC OF SINGAPORE, and Department of Mathematics and the Centre for Financial Engineering, National University of Singapore, Singapore, REPUBLIC OF SINGAPORE (e-mail: matsuny@nus.edu.sg) , SG |
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| Abstract: | 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 -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.
Received: October 29, 2001; revised version: April 24, 2002
RID="*"
ID="*" 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
Kübler 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.
Correspondence to: P.J. Hammond |
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| 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 |
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