Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case
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- Hammond, P. & Sun, Y. Econ Theory (2003) 21: 743. doi:10.1007/s00199-002-0302-y
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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.