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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 Toulouse School of Economics (TSE) in its series TSE Working Papers with number 12-303.

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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:tse:wpaper:25815
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  1. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer, vol. 48(2), pages 243-273, October.
  2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  3. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  4. 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.
  5. Jin-Tan Liu & Meng-Wen Tsou & James Hammitt, 2007. "Health Information and Subjective Survival Probability: Evidence from Taiwan," NBER Working Papers 12864, National Bureau of Economic Research, Inc.
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  7. 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.
  8. Gollier, Christian & Schlesinger, Harris, 1996. "Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach," Economic Theory, Springer, vol. 7(2), pages 359-63, February.
  9. Jianjun Miao & NENGJIU JU, 2010. "Ambiguity, Learning, And Asset Returns," Boston University - Department of Economics - Working Papers Series WP2010-031, Boston University - Department of Economics.
  10. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
  11. Blazenko, George, 1985. "The Design of an Optimal Insurance Policy: Note," American Economic Review, American Economic Association, vol. 75(1), pages 253-55, March.
  12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  13. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
  14. 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.
  15. Sujoy Mukerji & Peter Klibanoff & Massimo Marinacci, 2011. "Definitions of Ambiguous Events and the Smooth Ambiguity Model," Economics Series Working Papers 525, University of Oxford, Department of Economics.
  16. Hideki Iwaki & Yusuke Osaki, 2014. "The dual theory of the smooth ambiguity model," Economic Theory, Springer, vol. 56(2), pages 275-289, June.
  17. Vassili Vergopoulos, 2011. "Dynamic consistency for non-expected utility preferences," Economic Theory, Springer, vol. 48(2), pages 493-518, October.
  18. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  19. 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.
  20. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  21. 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.
  22. Shahidi, Niousha & Carlier, Guillaume & Dana, Rose-Anne, 2003. "Efficient Insurance Contracts under Epsilon-Contaminated Utilities," Economics Papers from University Paris Dauphine 123456789/5463, Paris Dauphine University.
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