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The design of an optimal insurance contract for irreplaceable commodities

Author

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  • Rachel J. Huang

    (Department of Finance, Ming Chuan University, Taiwan, e-mail: rachel@mcu.edu.tw)

  • Larry Y. Tzeng

    (Department of Finance, National Taiwan University, Taiwan)

Abstract

This paper discusses optimal insurance contract for irreplaceable commodities. To describe the dual impacts on individuals when a loss occurs to the insured irreplaceable commodities, we use a state-dependent and bivariate utility function, which includes both the monetary wealth and sentimental value as two arguments. We show that over (full, partial) insurance is optimal when a decrease in sentimental value will increase (not change, decrease, respectively) the marginal utility of monetary wealth. Moreover, a non-zero deductible exists even without administration costs. Furthermore, we demonstrate that a positive fixed reimbursement is optimal if (1) the premium is actuarially fair, (2) the monetary loss is a constant, and (3) the utility function is additively separable and the marginal utility of money is higher in the loss state than in the no-loss state. We also characterize comparative statics of fixed-reimbursement insurance under an additively separable preference assumption. The Geneva Risk and Insurance Review (2006) 31, 11–21. doi:10.1007/s10713-006-9464-z

Suggested Citation

  • Rachel J. Huang & Larry Y. Tzeng, 2006. "The design of an optimal insurance contract for irreplaceable commodities," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(1), pages 11-21, July.
    • Handle: RePEc:pal:genrir:v:31:y:2006:i:1:p:11-21
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    References listed on IDEAS

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    1. Lewbel, Arthur, 1996. "Aggregation without Separability: A Generalized Composite Commodity Theorem," American Economic Review, American Economic Association, vol. 86(3), pages 524-543, June.
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    Cited by:

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    2. Yichun Chi & Xun Yu Zhou & Sheng Chao Zhuang, 2020. "Variance Contracts," Papers 2008.07103, arXiv.org.
    3. Markus Rieger‐Fels, 2024. "Why do people buy insurance? A modern answer to an old question," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 27(1), pages 89-114, April.
    4. Chi, Yichun & Zhou, Xun Yu & Zhuang, Sheng Chao, 2024. "Variance insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 62-82.
    5. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    6. Fels, Markus, 2019. "Risk Attitudes with State-Dependent Indivisibilities in Consumption," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203489, Verein für Socialpolitik / German Economic Association.
    7. Lee, Hangsuck & Lee, Minha & Hong, Jimin, 2022. "Optimal insurance under moral hazard in loss reduction," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    8. Seog, S. Hun & Hong, Jimin, 2024. "Moral hazard in loss reduction and state-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 151-168.

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