The impact of a and b value uncertainty on loss estimation in the reinsurance industry

D. Liechti, E. Ruettener, S. Eugster, R. Streit


In the reinsurance industry different probabilistic models are currently used for seismic risk analysis. A credible loss estimation of the insured values depends on seismic hazard analysis and on the vulnerability functions of the given structures. Besides attenuation and local soil amplification, the earthquake occurrence model (often represented by the Gutenberg and Richter relation) is a key element in the analysis. However, earthquake catalogues are usually incomplete, the time of observation is too short and the data themselves contain errors. Therefore, a and b values can only be estimated with uncertainties. The knowledge of their variation provides a valuable input for earthquake risk analysis, because they allow the probability distribution of expected losses (expressed by Average Annual Loss (AAL)) to be modelled. The variations of a and b have a direct effect on the estimated exceeding probability and consequently on the calculated loss level. This effect is best illustrated by exceeding probability versus loss level and AAL versus magnitude graphs. The sensitivity of average annual losses due to different a to b ratios and magnitudes is obvious. The estimation of the variation of a and b and the quantification of the sensitivity of calculated losses are fundamental for optimal earthquake risk management. Ignoring these uncertainties means that risk management decisions neglect possible variations of the earthquake loss estimations.


Completeness;seismic risk;b-value;average annual loss;insurance

Full Text:



We use cookies to ensure that we give you the best experience on our website. If you continue to use this site we will assume that you are happy with it (Read more).

Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X