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The Design of Optimal Insurance Contracts: A Topological Approach

Author

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  • Sandrine Spaeter

    ([1] University Louis Pasteur, LARGE-38 Boulevard d'Anvers, 67 070 Strasbourg, France [2] CREST/ENSAE, Malakoff, France)

  • Patrick Roger

    ([1] University Louis Pasteur, LARGE-38 Boulevard d'Anvers, 67 070 Strasbourg, France [2] CREST/ENSAE, Malakoff, France)

Abstract

This article deals with the optimal design of insurance contracts when the insurer faces administrative costs. If the literature provides many analyses of risk sharing with such costs, it is often assumed that these costs are linear. Furthermore, mathematical tools or initial conditions differ from one paper to another. We propose here a unified framework in which the problem is presented and solved as an infinite dimensional optimization program on a functional vector space equipped with an original norm. This general approach leads to the optimality of contracts lying on the frontier of the indemnity functions set. This frontier includes, in particular, contracts with a deductible, with total insurance and the null vector. Hence, we unify the existing results and point out some extensions. The Geneva Papers on Risk and Insurance Theory (1997) 22, 5–19. doi:10.1023/A:1008654729504

Suggested Citation

  • Sandrine Spaeter & Patrick Roger, 1997. "The Design of Optimal Insurance Contracts: A Topological Approach," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 22(1), pages 5-19, June.
    • Handle: RePEc:pal:genrir:v:22:y:1997:i:1:p:5-19
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    Citations

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    Cited by:

    1. Knut K. Aase, 2017. "Optimal Insurance Policies in the Presence of Costs," Risks, MDPI, vol. 5(3), pages 1-17, September.
    2. Johanna Etner & Sandrine Spaeter, 2010. "The impact of ambiguity on health prevention and insurance," Working Papers of BETA 2010-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    3. Michael Breuer, 2006. "Optimal insurance contracts without the non-negativity constraint on indemnities: revisited," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(1), pages 5-9, July.
    4. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    5. Jean-Gabriel Lauzier, 2021. "Insurance design and arson-type risks," Papers 2112.06817, arXiv.org.
    6. Kaluszka, Marek, 2004. "An extension of Arrow's result on optimality of a stop loss contract," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 527-536, December.
    7. Hung-Hsi Huang, 2006. "Optimal insurance contract under a value-at-risk constraint," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 91-110, December.
    8. Constantin Anghelache & Madalina Gabriela Anghel & Alexandru Ursache, 2015. "The Optimal Co-Insurance Model," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 6, pages 305-308, December.
    9. Constantin Anghelache & Madalina Gabriela Anghel & Marius Popovici, 2015. "Comparative Analysis In Co-Insurance Model," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 6, pages 10-12, December.

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