Advanced Search
MyIDEAS: Login to save this paper or follow this series

Monotone equimeasurable rearrangements with non-additive probabilities

Contents:

Author Info

  • Ghossoub, Mario

Abstract

In the classical theory of monotone equimeasurable rearrangements of functions, “equimeasurability” (i.e. the fact the two functions have the same distribution) is defined relative to a given additive probability measure. These rearrangement tools have been successfully used in many problems in economic theory dealing with uncertainty where the monotonicity of a solution is desired. However, in all of these problems, uncertainty refers to the classical Bayesian understanding of the term, where the idea of ambiguity is absent. Arguably, Knighitan uncertainty, or ambiguity is one of the cornerstones of modern decision theory. It is hence natural to seek an extension of these classical tools of equimeasurable rearrangements to situations of ambiguity. This paper introduces the idea of a monotone equimeasurable rearrangement in the context of non-additive probabilities, or capacities that satisfy a property that I call strong nonatomicity. The latter is a strengthening of the notion of nonatomicity, and these two properties coincide for additive measures and for submodular (i.e. concave) capacities. To illustrate the usefulness of these tools in economic theory, I consider an application to a problem arising in the theory of production under uncertainty.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://mpra.ub.uni-muenchen.de/37629/
File Function: original version
Download Restriction: no

Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37629.

as in new window
Length:
Date of creation: 07 Oct 2011
Date of revision: 23 Mar 2012
Handle: RePEc:pra:mprapa:37629

Contact details of provider:
Postal: Schackstr. 4, D-80539 Munich, Germany
Phone: +49-(0)89-2180-2219
Fax: +49-(0)89-2180-3900
Web page: http://mpra.ub.uni-muenchen.de
More information through EDIRC

Related research

Keywords: Ambiguity; Capacity; Non-Additive Probability; Choquet Integral; Monotone Equimeasurable Rearrangement; Production under Uncertainty;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 19, July.
  2. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
  3. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  4. Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
  5. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Carlier, Guillaume & Lachapelle, Aimé, 2011. "A numerical approach for a class of risk-sharing problems," Economics Papers from University Paris Dauphine 123456789/3821, Paris Dauphine University.
  7. Adriana Castaldo & Massimo Marinacci, 2002. "A Lusin theorem for a class of Choquet capacities," Statistical Papers, Springer, vol. 43(1), pages 137-142, January.
  8. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
  9. Ghirardato, Paolo, 1995. "On Independence For Non-Additive Measures, With a Fubini Theorem," Working Papers 940, California Institute of Technology, Division of the Humanities and Social Sciences.
  10. Galichon, Alfred & Dana, Rose-Anne & Carlier, Guillaume, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Economics Papers from University Paris Dauphine 123456789/9713, Paris Dauphine University.
  11. Dana, Rose-Anne & Carlier, Guillaume, 2011. "Optimal Demand for Contingent Claims when Agents have law Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2317, Paris Dauphine University.
  12. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235, April.
  13. Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
  14. repec:ebl:ecbull:v:7:y:2003:i:5:p:1-9 is not listed on IDEAS
  15. Carlier, G. & Dana, R.-A., 2005. "Existence and monotonicity of solutions to moral hazard problems," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 826-843, November.
  16. Dana, Rose-Anne, 2004. "Market behavior when preferences are generated by second-order stochastic dominance," Economics Papers from University Paris Dauphine 123456789/6697, Paris Dauphine University.
  17. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
  18. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
  19. Carlier, Guillaume & Dana, Rose-Anne, 2003. "Core of convex distortions of a probability," Economics Papers from University Paris Dauphine 123456789/5446, Paris Dauphine University.
  20. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  21. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
  22. Carlier, Guillaume & Dana, Rose-Anne, 2005. "Rearrangement inequalities in non-convex insurance models," Economics Papers from University Paris Dauphine 123456789/5389, Paris Dauphine University.
  23. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer, vol. 36(2), pages 189-223, August.
  24. Dana, Rose-Anne & Carlier, Guillaume, 2008. "Two-Persons Efficient Risk-Sharing and Equilibria for Concave Law-Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2348, Paris Dauphine University.
  25. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  26. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
  27. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
  28. Fabio Maccheroni & Massimo Marinacci, 2004. "A strong law of large numbers for capacities," ICER Working Papers - Applied Mathematics Series 28-2004, ICER - International Centre for Economic Research.
  29. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  30. Carlier, Guillaume & Dana, Rose-Anne, 2005. "Existence and monotonicity of solutions to moral hazard problems," Economics Papers from University Paris Dauphine 123456789/5371, Paris Dauphine University.
  31. Dana, R. A., 2004. "Market behavior when preferences are generated by second-order stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 619-639, September.
  32. Victor Chernozhukov & Iván Fernández-Val & Alfred Galichon, 2010. "Rearranging Edgeworth–Cornish–Fisher expansions," Economic Theory, Springer, vol. 42(2), pages 419-435, February.
  33. Lefort, Jean-Philippe & Chateauneuf, Alain, 2008. "Some Fubini Theorems on product σ-algebras for non-additive measures," Economics Papers from University Paris Dauphine 123456789/7324, Paris Dauphine University.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  2. Amarante, M & Ghossoub, M & Phelps, E, 2013. "Innovation, Entrepreneurship and Knightian Uncertainty," Working Papers 12241, Imperial College, London, Imperial College Business School.
  3. AMARANTE, Massimiliano & GHOSSOUB, Mario & PHELPS, Edmund, 2012. "Contracting for innovation under knightian uncertainty," Cahiers de recherche 2012-15, Universite de Montreal, Departement de sciences economiques.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:37629. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.