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Optimal insurance with mean-deviation measures

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  • Boonen, Tim J.
  • Han, Xia

Abstract

This paper studies an optimal insurance contracting problem in which the preferences of the decision maker are given by the sum of the expected loss and a convex, increasing function of a deviation measure. As for the deviation measure, our focus is on convex signed Choquet integrals (such as the Gini coefficient and a convex distortion risk measure minus the expected value) and on the standard deviation. We find that if the expected value premium principle is used, then stop-loss indemnities are optimal, and we provide a precise characterization of the corresponding deductible. Moreover, if the premium principle is based on Value-at-Risk or Expected Shortfall, then a particular layer-type indemnity is optimal, in which there is coverage for small losses up to a limit, and additionally for losses beyond another deductible. The structure of these optimal indemnities remains unchanged if there is a limit on the insurance premium budget. If the unconstrained solution is not feasible, then the deductible is increased to make the budget constraint binding. We provide several examples of these results based on the Gini coefficient and the standard deviation.

Suggested Citation

  • Boonen, Tim J. & Han, Xia, 2024. "Optimal insurance with mean-deviation measures," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 1-24.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:1-24
    DOI: 10.1016/j.insmatheco.2024.05.005
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    References listed on IDEAS

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    More about this item

    Keywords

    Risk management; Deviation measures; Mean-deviation measures; Monotonicity; Optimal insurance; Stop-loss indemnities; Budget constraint;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • 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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