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The design of an optimal insurance contract for irreplaceable commodities


  • Rachel J. Huang

    (Department of Finance, Ming Chuan University, Taiwan, e-mail:

  • Larry Y. Tzeng

    (Department of Finance, National Taiwan University, Taiwan)


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

    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.
    2. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    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.
    4. Philip J. Cook & Daniel A. Graham, 1977. "The Demand for Insurance and Protection: The Case of Irreplaceable Commodities," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 143-156.
    5. Diewert, W. E. & Wales, T. J., 1995. "Flexible functional forms and tests of homogeneous separability," Journal of Econometrics, Elsevier, vol. 67(2), pages 259-302, June.
    6. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
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    Cited by:

    1. Marielle Brunette & Stéphane Couture, 2018. "Risk management activities of a non-industrial private forest owner with a bivariate utility function," Review of Agricultural, Food and Environmental Studies, Springer, vol. 99(3), pages 281-302, December.
    2. 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.

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