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Ambiguity on the insurer’s side: The demand for insurance

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  • Amarante, Massimiliano
  • Ghossoub, Mario
  • Phelps, Edmund

Abstract

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., Hogarth and Kunreuther, 1989). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then optimal indemnity schedules exist and are monotonic. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., Huberman et al., 1983). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow (1971) on the optimality of the deductible indemnity schedule.

Suggested Citation

  • Amarante, Massimiliano & Ghossoub, Mario & Phelps, Edmund, 2015. "Ambiguity on the insurer’s side: The demand for insurance," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 61-78.
  • Handle: RePEc:eee:mateco:v:58:y:2015:i:c:p:61-78
    DOI: 10.1016/j.jmateco.2015.03.008
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    References listed on IDEAS

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    1. repec:gam:jrisks:v:4:y:2016:i:1:p:8:d:66161 is not listed on IDEAS
    2. Ghossoub, Mario, 2015. "Vigilant measures of risk and the demand for contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 27-35.
    3. Mario Ghossoub, 2016. "Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-28, August.
    4. Dietz, Simon & Walker, Oliver, 2017. "Ambiguity and insurance: capital requirements andpremiums," LSE Research Online Documents on Economics 68469, London School of Economics and Political Science, LSE Library.
    5. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-11, July.
    6. Massimiliano Amarante & Mario Ghossoub, 2016. "Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer," Risks, MDPI, Open Access Journal, vol. 4(1), pages 1-27, March.
    7. Mingli Zheng & Chong Wang & Chaozheng Li, 2016. "Insurance Contracts with Adverse Selection When the Insurer Has Ambiguity about the Composition of the Consumers," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 179-206, May.

    More about this item

    Keywords

    Optimal insurance; Deductible; Ambiguity; Choquet integral; Distorted probabilities;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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