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Optimal insurance under maxmin expected utility

Author

Listed:
  • Corina Birghila

    (Otto-von-Guericke University Magdeburg)

  • Tim J. Boonen

    (University of Amsterdam)

  • Mario Ghossoub

    (University of Waterloo)

Abstract

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the maxmin expected utility model of Gilboa and Schmeidler (J. Math. Econ. 18:141–153, 1989), whereas the insurer is a (risk-averse or risk-neutral) expected-utility maximiser. We characterise optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, of marginal utility of wealth, of belief heterogeneity, as well as of ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how a singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.

Suggested Citation

  • Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:2:d:10.1007_s00780-023-00497-y
    DOI: 10.1007/s00780-023-00497-y
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    References listed on IDEAS

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    3. Bradley, Richard, 2024. "Catastrophe insurance decision making when the science is uncertain," LSE Research Online Documents on Economics 122508, London School of Economics and Political Science, LSE Library.
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    5. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.

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    More about this item

    Keywords

    Optimal insurance; Ambiguity; Multiple priors; Maxmin expected utility; Heterogeneous beliefs;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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