General bounds for the deficit distribution at ruin in the Sparre Andersen model

Abstract We present constructive methods that give upper and lower bounds of Ψ , the insurer’s deficit distribution at ruin time in the Sparre Andersen model. The methodology effectively provides monotone sequences of upper and lower bounds of Ψ , and those sequences converge to Ψ with exponential rate. Several new lower and upper bounds of Ψ are given. As an example, we introduce new bounds of the deficit distribution at ruin when the claim distribution satisfies the new better/worse than used property. We show that some of the examined lower and upper bounds of Ψ may coincide with the exact values of the considered probability.