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Ambiguity and insurance: robust capital requirements and premiums

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  • Oliver Walker
  • Simon Dietz

Abstract

Many insurance and reinsurance contracts are contingent on events such ashurricanes, terrorist attacks or political upheavals whose probabilities are not known with precision. There is a body of experimental evidence showing thathigher premiums are charged for these �ambiguous� contracts, which may in turn inhibit (re)insurance transactions, but little research analysing explicitlyhow and why premiums are loaded in this way. In this paper we model the effect of ambiguity on the capital requirement of a (re)insurer whose objectives are profit maximisation and robustness. The latter objective means that it musthold enough capital to meet a survival constraint across a range of availableestimates of the probability of ruin. We provide characterisations of when onebook of insurance is more ambiguous than another and formally explore thecircumstances in which a more ambiguous book requires at least as large acapital holding. This analysis allows us to derive several explicit formulae forthe price of ambiguous insurance contracts, each of which identifies the extraambiguity load.

Suggested Citation

  • Oliver Walker & Simon Dietz, 2012. "Ambiguity and insurance: robust capital requirements and premiums," GRI Working Papers 97, Grantham Research Institute on Climate Change and the Environment.
  • Handle: RePEc:lsg:lsgwps:wp97
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    References listed on IDEAS

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    1. Kunreuther, Howard & Hogarth, Robin & Meszaros, Jacqueline, 1993. "Insurer Ambiguity and Maarket Failure," Journal of Risk and Uncertainty, Springer, vol. 7(1), pages 71-87, August.
    2. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2013. "Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis," Econometrica, Econometric Society, vol. 81(3), pages 1075-1113, May.
    3. Zhu, Wenge, 2011. "Ambiguity aversion and an intertemporal equilibrium model of catastrophe-linked securities pricing," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 38-46, July.
    4. Kunreuther, Howard & Meszaros, Jacqueline & Hogarth, Robin M. & Spranca, Mark, 1995. "Ambiguity and underwriter decision processes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 337-352, May.
    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. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    7. 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.
    8. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    9. Hogarth, Robin M & Kunreuther, Howard, 1989. "Risk, Ambiguity, and Insurance," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 5-35, April.
    10. Kunreuther, Howard C. & Michel-Kerjan, Erwann O., 2011. "At War with the Weather: Managing Large-Scale Risks in a New Era of Catastrophes," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262516543, January.
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