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Implementing Arrow-Debreu equilibria by trading infinitely lived securities

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  • K. Huang
  • Z. Liu

Abstract

We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu equilibria with transfers. Transfers are equal to the value of price bubbles on initial portfolio holdings. Price bubbles may arise in sequential equilibrium under the wealth constraint, but with essentially bounded portfolios.

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Bibliographic Info

Paper provided by Utah State University, Department of Economics in its series Working Papers with number 2000-21.

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Length: 31 pages
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Handle: RePEc:usu:wpaper:2000-21

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Keywords: Arrow-Debreu equilibrium; security markets equilibrium; price bubbles; transfers;

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References

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  1. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  2. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  3. Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
    • Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September.
  4. Kocherlakota, N.R., 1990. "Bubbles and Constraints on Debt Accumulation," Working Papers 90-29, University of Iowa, Department of Economics.
  5. Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," DELTA Working Papers 92-26, DELTA (Ecole normale supérieure).
  6. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-77, October.
  7. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series 05-2001, ICER - International Centre for Economic Research.
  8. Magill, M. & Quinzii, M., 1993. "Icomplete Markets Over an Infinite Horizon: Long-Lived Securities and Speculative Bubbles," Papers 9321, Southern California - Department of Economics.
  9. L. Wade, 1988. "Review," Public Choice, Springer, vol. 58(1), pages 99-100, July.
  10. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
  11. Monique Florenzano & Pascal Gourdel, 1996. "Incomplete Markets In Infinite Horizon: Debt Constraints Versus Node Prices," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 167-196.
  12. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  13. Kandori, Michihiro, 1988. "Equivalent Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 401-17, August.
  14. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer, vol. 15(2), pages 253-278.
  15. Duffie, J Darrell & Huang, Chi-fu, 1985. "Implementing Arrow-Debreu Equilibria by Continuous Trading of Few Long-lived Securities," Econometrica, Econometric Society, vol. 53(6), pages 1337-56, November.
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Cited by:
  1. G. Bloise & J.H. Dreze & H.M. Polemarchakis, 2002. "Money and Indeterminacy Over an Infinite Horizon," Working Papers 2002-12, Brown University, Department of Economics.
  2. Marco Bassetto & Thomas Sargent, 2005. "Politics and Efficiency of Separating Capital and Ordinary Government Budgets," NBER Working Papers 11030, National Bureau of Economic Research, Inc.
  3. Patarick Leoni, 2006. "Market Power, Survival and Accuracy of Predictions in Financial Markets," Economics, Finance and Accounting Department Working Paper Series n1701106, Department of Economics, Finance and Accounting, National University of Ireland - Maynooth.

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