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Intertemporal Equilibria with Knightian Uncertainty

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  • Rose-Anne Dana

    (CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine)

  • Frank Riedel

    ()
    (Institute of Mathematical Economics, Bielefeld University)

Abstract

We study a dynamic and infinite-dimensional model with Knightian uncertainty modeled by incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and use the same subjective interest rate. Interior efficient allocations 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 uncertainty 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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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-440.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 440.

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Length: 30 pages
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:bie:wpaper:440

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Related research

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

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References

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  1. 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.
  2. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, Econometric Society, vol. 76(5), pages 1167-1190, 09.
  3. 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.
  4. 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.
  5. 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.
  6. 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 qt6m42r5rr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  7. 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.
  8. 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.
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  10. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, Econometric Society, vol. 77(3), pages 857-908, 05.
  11. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
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  14. 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.
  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. 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.
  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. 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.
  19. 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.
  20. 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.
  21. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  22. Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, Elsevier, vol. 130(1), pages 283-295, September.
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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. 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.
  4. Patrick Beißner, 2013. "Radner equilibria under ambiguous volatility," Working Papers, Bielefeld University, Center for Mathematical Economics 493, Bielefeld University, Center for Mathematical Economics.
  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. repec:ipg:wpaper:201420 is not listed on IDEAS

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