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Coherence without Additivity

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  • Enrico Diecidue

    ()

  • Fabio Maccheroni

    ()

Abstract

The Dutch book argument is a coherence condition for the existence of subjective probabilities. This note gives a general framework of analysis for this argument in a nonadditive probability setting. Particular cases are given by comonotonic and affinely related Dutch books that lead to Choquet expectations and Min expectations.

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File URL: http://www.icer.it/docs/wp2002/maccheroni10-02.pdf
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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 10-2002.

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Length: 10 pages
Date of creation: Feb 2002
Date of revision:
Handle: RePEc:icr:wpmath:10-2002

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Related research

Keywords: Coherence; Dutch Book; Constant Linearity; Choquet Expectation; Multiple Priors;

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References

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  1. Adriana Castaldo & Massimo Marinacci, 2001. "Random correspndences as bundles of random variables," ICER Working Papers - Applied Mathematics Series 12-2001, ICER - International Centre for Economic Research.
  2. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
  3. Maitreesh Ghatak & Massimo Morelli & Tomas Sjoström, 2001. "Credit rationing, wealth inequality, and allocation of talent," ICER Working Papers - Applied Mathematics Series 23-2001, ICER - International Centre for Economic Research.
  4. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research.
  5. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," POLIS Working Papers 5, Institute of Public Policy and Public Choice - POLIS.
  6. Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research.
  7. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  8. Fabio Maccheroni, 2000. "Yaari dual theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 30-2001, ICER - International Centre for Economic Research, revised Oct 2001.
  9. Massimo Marinacci & Luigi Montrucchio, 2001. "Subcalculus for set functions and cores of TU games," ICER Working Papers - Applied Mathematics Series 09-2001, ICER - International Centre for Economic Research.
  10. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research.
  11. Domenico Menicucci, 2001. "Optimal two-object auctions with synergies," ICER Working Papers - Applied Mathematics Series 18-2001, ICER - International Centre for Economic Research.
  12. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
  13. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
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Citations

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Cited by:
  1. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
  2. Thibault Gajdos & Eric Maurin, 2004. "Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085940, HAL.
  3. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  4. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
  5. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research.
  6. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
  7. Andrea Capotorti & Giulianella Coletti & Barbara Vantaggi, 2008. "Preferences Representable by a Lower Expectation: Some Characterizations," Theory and Decision, Springer, vol. 64(2), pages 119-146, March.
  8. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
  9. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
  10. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
  11. Enrico Diecidue & Dolchai La-ornual, 2009. "Reconciling support theory and the book-making principle," Journal of Risk and Uncertainty, Springer, vol. 38(3), pages 173-190, June.
  12. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.

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