Approximations of Ruin Probability by Di-Atomic or Di-Exponential Claims

Abstract

AbstractThe sensitivity of the ruin probability depending on the claim size distribution has been the topic of several discussion papers in recent ASTIN Bulletins. This discussion was initiated by a question raised by Schmitter at the ASTIN Colloquium 1990 and attempts to make further contributions to this problem. We find the necessary and sufficient conditions for fitting three given moments by diatomic and diexponential distributions. We consider three examples drawn from fire (large spread), individual life (medium spread) and group life (small spread) insurance data, fit them with diatomics and diexponentials whenever the necessary and sufficient conditions are met, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature. Finally we propose using diatomic and diexponential claim distributions as tools to study the Schmitter problem.