Approximate formulas for calculation of the optimal level of deductible

In the paper we considered a problem of definition of the optimal level of deductible in the case of excess-of-loss insurance. Theorem 1 concerns the case when the function of excess-of-loss insurance does not depend on the type of utility function. Theorem 3 concerns the case when the insurance premium depends on the level of deductible. For each case we defined approximate formulas for calculation of the optimal level of deductible (theorems 2, 4, and 5).