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The design of an optimal insurance contract for irreplaceable commodities

Author

Listed:
  • 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. Philip J. Cook & Daniel A. Graham, 1977. "The Demand for Insurance and Protection: The Case of Irreplaceable Commodities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 143-156.
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    8. Béatrice Rey & Jean-Charles Rochet, 2004. "Health and Wealth: How do They Affect Individual Preferences?*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 29(1), pages 43-54, June.
    9. Louis Eeckhoudt & Olivier Mahul & John Moran, 2003. "Fixed‐Reimbursement Insurance: Basic Properties and Comparative Statics," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(2), pages 207-218, June.
    10. Louis R. Eeckhoudt & Olivier Mahul & John Moran, 2003. "Fixed-reimbursement insurance : basic properties and comparative statics," Post-Print hal-01952092, HAL.
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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. Fels, Markus, 2021. "Why Do People Buy Insurance? A Modern Answer to an Old Question," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242418, Verein für Socialpolitik / German Economic Association.
    4. 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).
    5. Fels, Markus, 2019. "Risk attitudes with state-dependent indivisibilities in consumption," Ruhr Economic Papers 805, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.

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