Abstract
The 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.
KEYWORDS Ruin probability; diatomic distribution; diexponential distribution.
Volume
22:2
Page
235-246
Year
1992
Categories
Financial and Statistical Methods
Loss Distributions
Extreme Values
Actuarial Applications and Methodologies
Regulation and Law
Solvency
Actuarial Applications and Methodologies
Dynamic Risk Modeling
Solvency Analysis
Business Areas
Fire and Allied Lines
Business Areas
Other Lines of Business
Practice Areas
Risk Management
Publications
ASTIN Bulletin
