Lower and upper bounds for survival functions of the smallest and largest claim amounts in layer coverages.

We consider n risks X 1 , X 2 , ... , X n insured by a layer coverage with deductibles and limits given by (d 1 , l 1) , ... , (d n , l n) , respectively. We investigate the optimal allocation of insurance layers from the viewpoint of the insurer. We derive lower and upper bounds for the survival function of the smallest and largest claim amounts using the first stochastic dominance order. We find that assigning a small deductible and a large limit to large risks increases (decreases) stop-loss premiums of the largest (smallest) claim amounts. [ABSTRACT FROM AUTHOR]