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Optimal insurance design of ambiguous risks

  • Gollier, Christian

We examine the characteristics of the optimal insurance contract under linear transaction cost and an ambiguous distribution of losses. Under the standard expected utility model, we know from Arrow (1965) that it contains a straight deductible. In this paper, we assume that the policyholder is ambiguity-averse in the sense of Klibanoff, Marinacci and Mukerji (2005). The optimal contract depends upon the structure of the ambiguity. For example, if the set of possible priors can be ranked according to the monotone likelihood ratio order, the optimal contract contains a disappearing deductible. We also show that the policyholder’s ambiguity aversion can reduce the optimal insurance coverage.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 718.

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Date of creation: May 2012
Date of revision: Jan 2013
Publication status: Published in Economic Theory, vol. 57, n°3, Springer Berlin / Heidelberg, novembre 2014, p. 555-576.
Handle: RePEc:ide:wpaper:25812
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  1. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  2. Jin-Tan Liu & Meng-Wen Tsou & James K. Hammitt, 2007. "Health Information and Subjective Survival Probability: Evidence from Taiwan," Journal of Risk Research, Taylor & Francis Journals, vol. 10(2), pages 149-175, March.
  3. Christian Gollier & Harris Schlesinger, 1996. "Arrow's theorem on the optimality of deductibles: A stochastic dominance approach (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363.
  4. Ian Jewitt, 1987. "Risk Aversion and the Choice Between Risky Prospects: The Preservation of Comparative Statics Results," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 73-85.
  5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  6. G. Carlier & R.A. Dana & N. Shahidi, 2003. "Efficient Insurance Contracts under Epsilon-Contaminated Utilities," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 28(1), pages 59-71, June.
  7. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2006. "Recursive Smooth Ambiguity Preferences," Carlo Alberto Notebooks 17, Collegio Carlo Alberto, revised 2008.
  8. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
  9. Nengjiu Ju & Jianjun Miao, . "Ambiguity, Learning, and Asset Returns," Boston University - Department of Economics - Working Papers Series wp2009-014, Boston University - Department of Economics.
  10. Hideki Iwaki & Yusuke Osaki, 2014. "The dual theory of the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 275-289, June.
  11. Vassili Vergopoulos, 2011. "Dynamic consistency for non-expected utility preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 493-518, October.
  12. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1991. "Increases in risk and deductible insurance," Journal of Economic Theory, Elsevier, vol. 55(2), pages 435-440, December.
  13. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2010. "Alpha as Ambiguity: Robust Mean-Variance Portfolio Analysis," Working Papers 373, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  14. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "Definitions of ambiguous events and the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 399-424, October.
  15. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
  16. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  17. David Alary & Christian Gollier & Nicolas Treich, 2013. "The Effect of Ambiguity Aversion on Insurance and Self‐protection," Economic Journal, Royal Economic Society, vol. 123(12), pages 1188-1202, December.
  18. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  19. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
  20. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  21. Blazenko, George, 1985. "The Design of an Optimal Insurance Policy: Note," American Economic Review, American Economic Association, vol. 75(1), pages 253-55, March.
  22. repec:dau:papers:123456789/5463 is not listed on IDEAS
  23. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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