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We find the optimal indemnity to minimize the probability of ruin whenpremium is calculated according to the distortion premium principle with aproportional risk load, and admissible indemnities are such that both theindemnity and retention are non-decreasing functions of the underlying loss. Wereformulate the problem with the inverse survival function as the controlvariable and show that deductible insurance with maximum limit is optimal. Ourmain contribution is in solving this problem via the inverse survival function.

Optimal Insurance to Minimize the Probability of Ruin: Inverse Survival Function Formulation