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The design of an optimal insurance contract for irreplaceable commodities

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  • Rachel Huang
  • Larry Tzeng

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. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Rachel Huang & Larry Tzeng, 2006. "The design of an optimal insurance contract for irreplaceable commodities," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(1), pages 11-21, July.
    • Handle: RePEc:kap:geneva:v:31:y:2006:i:1:p:11-21
    DOI: 10.1007/s10713-006-9464-z
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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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    3. 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.
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    Cited by:

    1. Yichun Chi & Xun Yu Zhou & Sheng Chao Zhuang, 2020. "Variance Contracts," Papers 2008.07103, arXiv.org.
    2. Marielle Brunette & Stephane Couture, 2018. "Risk management activities of a non-industrial privateforest owner with a bivariate utility function," Review of Agricultural, Food and Environmental Studies, INRA Department of Economics, vol. 99(3-4), pages 281-302.
    3. 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.
    4. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    5. 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.
    6. 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).

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