The design of an optimal insurance contract for irreplaceable commodities

Rachel Huang and Larry Y. Tzeng
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Larry Y. Tzeng: Department of Finance, National Taiwan University, Taiwan

The Geneva Risk and Insurance Review, 2006, vol. 31, issue 1, 21 pages

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

Date: 2006
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