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Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional

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Listed:
  • Jingyi Cao
  • Dongchen Li
  • Virginia R. Young
  • Bin Zou

Abstract

We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.

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  • Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2024. "Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional," Papers 2401.08094, arXiv.org.
    • Handle: RePEc:arx:papers:2401.08094
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    References listed on IDEAS

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    1. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    2. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    3. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    4. Xiaoqing Liang & Ruodu Wang & Virginia Young, 2021. "Optimal Insurance to Maximize RDEU Under a Distortion-Deviation Premium Principle," Papers 2107.02656, arXiv.org, revised Feb 2022.
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