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Intertemporal Equilibria with Knightian Uncertainty

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  • Riedel, Frank
  • Dana, Rose-Anne

Abstract

We study a dynamic and in nite{dimensional model with Knightian uncertainty modeled by incomplete multiple prior preferences. In in- terior e cient allocations, agents share a common risk{adjusted prior and use the same subjective interest rate. Interior e cient alloca- tions and equilibria coincide with those of economies with subjective expected utility and priors from the agents' multiple prior sets. We show that the set of equilibria with inertia contains the equilibria of the economy with variational preferences anchored at the initial endowments. A case study in an economy without aggregate uncer- tainty shows that risk is fully insured, while uncertainty can remain fully uninsured. Pessimistic agents with Gilboa{Schmeidler's max-min preferences would fully insure risk and uncertainty.

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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/5375.

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Date of creation: Jun 2010
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Handle: RePEc:dau:papers:123456789/5375

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Keywords: No Trade; General Equilibrium Theory; Incomplete Preferences; Ambiguity; Knightian Uncertainty;

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References

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  1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, Econometric Society, vol. 74(6), pages 1447-1498, November.
  2. Leandro Nascimento & Gil Riella, 2009. "A Class of Incomplete and Ambiguity Averse Preferences," Working Papers Series, Central Bank of Brazil, Research Department 180, Central Bank of Brazil, Research Department.
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  4. Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information, EconWPA 0201001, EconWPA.
  5. Zengjing Chen & Larry G. Epstein, 2000. "Ambiguity, risk and asset returns in continuous time," RCER Working Papers 474, University of Rochester - Center for Economic Research (RCER).
  6. Larry G. Epstein & Massimo Marinacci, 2006. "Mutual Absolute Continuity of Multiple Priors," Carlo Alberto Notebooks, Collegio Carlo Alberto 19, Collegio Carlo Alberto.
  7. Tallon, Jean-Marc & Dana, Rose-Anne & Chateauneuf, Alain, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5461, Paris Dauphine University.
  8. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, Econometric Society, vol. 78(2), pages 755-770, 03.
  9. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  10. Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 98.30, Université Panthéon-Sorbonne (Paris 1).
  11. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, Econometric Society, vol. 77(3), pages 857-908, 05.
  12. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, Elsevier, vol. 130(1), pages 283-295, September.
  13. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, Elsevier, vol. 113(1), pages 1-31, November.
  14. repec:hal:journl:halshs-00451997 is not listed on IDEAS
  15. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, Econometric Society, vol. 80(4), pages 1791-1808, 07.
  16. Faro, José Heleno, 2011. "Variational Bewley Preferences," Insper Working Papers, Insper Working Paper, Insper Instituto de Ensino e Pesquisa wpe_258, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  17. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 514-540, June.
  18. Shannon, Chris & Strzalecki, Tomasz & Rigotti, Luca, 2008. "Subjective Beliefs and Ex Ante Trade," Scholarly Articles 3637104, Harvard University Department of Economics.
  19. Easley, David & O'Hara, Maureen, 2010. "Liquidity and valuation in an uncertain world," Journal of Financial Economics, Elsevier, Elsevier, vol. 97(1), pages 1-11, July.
  20. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(3), pages 1054-1091, May.
  21. Dana, Rose-Anne, 2002. "On Equilibria when Agents Have Multiple Priors," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5456, Paris Dauphine University.
  22. repec:hal:journl:halshs-00174553 is not listed on IDEAS
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Citations

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Cited by:
  1. Rose-Anne Dana & Cuong Le Van, 2014. "Efficient allocations and Equilibria with short-selling and Incomplete Preferences," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020646, HAL.
  2. R.A Dana & Cuong Le Van, 2014. "Efficient allocations and Equilibria with short-selling and Incomplete Preferences," Working Papers, Department of Research, Ipag Business School 2014-061, Department of Research, Ipag Business School.
  3. Patrick Beißner, 2013. "Radner equilibria under ambiguous volatility," Working Papers 493, Bielefeld University, Center for Mathematical Economics.
  4. repec:ipg:wpaper:201420 is not listed on IDEAS
  5. Carlier, G. & Dana, R.-A., 2013. "Pareto optima and equilibria when preferences are incompletely known," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(4), pages 1606-1623.
  6. Rose-Anne Dana & Cuong Le Van, 2014. "Efficient allocations and Equilibria with short-selling and Incomplete Preferences," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 14041, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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