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Monte Carlo simulation of macroeconomic risk with a continuum agents: the general case

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Hammond, Peter J. and Sun, Yeneng (2007) Monte Carlo simulation of macroeconomic risk with a continuum agents: the general case. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.803).

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Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...

Abstract

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a ran-dom process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

H Social Sciences > HB Economic Theory
Q Science > QA Mathematics

Divisions:

Faculty of Social Sciences > Economics

Library of Congress Subject Headings (LCSH):

Monte Carlo method, Convergence (Economics), Probabilities, Stochastic processes, Macroeconomics, Risk -- Mathematical models

Series Name:

Warwick economic research papers

Publisher:

University of Warwick, Department of Economics

Place of Publication:

Coventry

Official Date:

June 2007

Dates:

Date	Event
June 2007	Published

Number:

No.803

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Realised As:

Hammond, P.J. and Sun, Y. (2008). Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case. Economic Theory, 36(2), pp. 303-325. http://wrap.warwick.ac.uk/id/eprint/29996

Related URLs:

Related item in WRAP

References:

[1] P. Billingsley, Probability and Measure, (3rd. edn.), John Wiley, New York, 1995.
[2] W. W. Bledsoe and A. P. Morse, Product measures, Transactions of the American Mathematical Society 79 (1955), 173{215.
[3] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, (3rd. edn.), Springer, New York, 1997.
[4] G. M. Constantinides and D. Duffie Asset pricing with heterogeneous consumers, Journal of Political Economy 104 (1996), 219{40.
[5] J. L. Doob, Stochastic processes depending on a continuous parameter, Transactions of the American Mathematical Society 42 (1937), 107{140.
[6] J. L. Doob, Stochastic Processes, John Wiley, New York, 1953.
[7] R. M. Dudley, Real Analysis and Probability, Chapman & Hall, New York, 1989.
[8] R. Durrett, Probability: Theory and Examples, (2nd. edn.), Wadsworth, Belmont, California, 1996.
[9] P. J. Hammond and Y. N. Sun, Monte Carlo simulation of macroeconomic risk with a continuum of agents: The symmetric case, Economic Theory 21 (2003), 743{766.
[10] P. J. Hammond and Y. N. Sun, Joint measurability and the one-way Fubini property for a continuum of independent random variables, Proceedings of the American Mathematical Society 134 (2006), 737{747.
[11] P. J. Hammond and Y. N. Sun, The essential equivalence of pairwise and mutual conditional independence, Probability Theory and Related Fields 135 (2006), 415{427.
[12] J. Heaton and D. J. Lucas, Evaluating the e�ects of incomplete markets on risk sharing and asset pricing, Journal of Political Economy 104 (1996), 443{487.
[13] J. Ho�mann-J�rgensen, The law of large numbers for non-measurable and non-separable random elements, Astérisque 131 (1985), 299{356.
[14] M. O. Jackson and I. Kremer, Envy-freeness and implementation in large economies, Review of Economic Design, forthcoming.
[15] K. Judd, The law of large numbers with a continuum of IID random variables. Journal of Economic Theory 35 (1985), 19{25.
[16] O. Kallenberg, Foundations of Modern Probability, (2nd. edn.), Springer, New York, 2002.
[17] R. McLean and A. Postlewaite, Informational size and incentive compatibility, Econometrica 70 (2002), 2421{2453.
[18] T. Palfrey and S. Srivastava, Private information in large economies, Journal of Economic Theory 39 (1986), 34{58.
[19] K. R. Parthasarathy, Probability Measures on Metric Spaces, New York, Academic Press, 1967.
[20] Y. N. Sun, A theory of hyper�nite processes: The complete removal of individual uncertainty via exact LLN, Journal of Mathematical Economics 29 (1998), 419{503.
[21] Y. N. Sun, The almost equivalence of pairwise and mutual independence and the duality with exchangeability, Probability Theory and Related Fields 112 (1998), 425{456.
[22] Y. N. Sun, The exact law of large numbers via Fubini extension and characterization of insurable risks, Journal of Economic Theory 126 (2006), 31{69.
[23] Y. N. Sun and N. C. Yannelis, Perfect competition in asymmetric information economies: Compatibility of effciency and incentives, Journal of Economic Theory 134 (2007), 175{194.