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Intertemporal equilibria with Knightian uncertainty

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  • Riedel, Frank
  • Dana, Rose-Anne

Abstract

We study a dynamic and infinite–dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk–adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agentsʼ multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.

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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/11268.

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Date of creation: 2013
Date of revision:
Publication status: Published in Journal of Economic Theory, 2013, Vol. 148, no. 4. pp. 1582-1605.Length: 23 pages
Handle: RePEc:dau:papers:123456789/11268

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Related research

Keywords: Dynamic general equilibrium; No trade; General equilibrium theory; Incomplete preferences; Ambiguity; Knightian uncertainty;

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References

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  1. repec:hal:journl:halshs-00174553 is not listed on IDEAS
  2. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  3. 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.
  4. Epstein, Larry G. & Marinacci, Massimo, 2007. "Mutual absolute continuity of multiple priors," Journal of Economic Theory, Elsevier, Elsevier, vol. 137(1), pages 716-720, November.
  5. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality in a Multiple Prior Model," Carlo Alberto Notebooks, Collegio Carlo Alberto 73, Collegio Carlo Alberto, revised 2008.
  6. 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.
  7. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  8. 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.
  9. Alain Chateauneuf & Rose Anne Dana & Jean-Marc Tallon, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00451997, HAL.
  10. 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.
  11. Shannon, Chris & Strzalecki, Tomasz & Rigotti, Luca, 2008. "Subjective Beliefs and Ex Ante Trade," Scholarly Articles 3637104, Harvard University Department of Economics.
  12. Nascimento, Leandro & Riella, Gil, 2011. "A class of incomplete and ambiguity averse preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(2), pages 728-750, March.
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  14. 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.
  15. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing beliefs: between agreeing and disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00174553, HAL.
  16. repec:hal:journl:halshs-00451997 is not listed on IDEAS
  17. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks, Collegio Carlo Alberto 12, Collegio Carlo Alberto, revised 2006.
  18. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, Econometric Society, vol. 70(4), pages 1403-1443, July.
  19. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, Econometric Society, vol. 77(3), pages 857-908, 05.
  20. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, Elsevier, vol. 130(1), pages 283-295, September.
  21. 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.
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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," 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.
  2. Patrick Beißner, 2013. "Radner equilibria under ambiguous volatility," Working Papers 493, Bielefeld University, Center for Mathematical Economics.
  3. repec:ipg:wpaper:201420 is not listed on IDEAS
  4. 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.
  5. 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.
  6. 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.

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