Insurance Choice Under Third Degree Stochastic Dominance

In this paper, we investigate the insurance choice of a risk-averse and prudent insured by assuming that the insurance premium is calculated by a general mean–variance principle. This general class of premium principles encompasses many widely used premium principles such as expected value, variance related, modified variance and mean value principles. We show that any admissible insurance contract, in which the marginal indemnity above a deductible minimum is decreasing in the loss and has a value greater than zero and less than one, is suboptimal to a dual change-loss insurance policy or a change-loss insurance policy, depending upon the coefficient of variation of the ceded loss. Especially for variance related premium principles, it is shown that the change-loss insurance is optimal. In addition to change-loss insurance, a numerical example illustrates that the dual change-loss insurance may also be an optimal choice when the insurance premium is calculated by mean value principle.