Statistiska institutionen
Stockholms universitet

ABSTRACT

   We present a study on risk analysis of rare events such as catastrophes by using expert assessments. There are usually not sufficient data on the catastrophes. Hence, the risk analysis of rare events requires other methods than the conventional statistics may offer. A pragmatic approach to analyse catastrophe risks is to use expert assessments. The risk analysis models in this thesis calibrate and aggregate the expert assessments concerning the future in a Bayesian framework. The assessment errors, which the models are based on, are assumed to have multivariate normal distribution. We discuss risk analysis models both when the assessment errors are assumed to be independent and dependent.
    An empirical study was performed on risk analysis of major civil aircraft accidents in Europe by using expert assessments. The main goal was to investigate how the above mentioned models worked in practice. The experts in the survey were from Swedish Aviation Administration, the Board of Accident Investigation in Sweden, the airline company SAS and the reinsurance company Skandia International which has aviation underwriting. The expert assessments were about the number of accidents and fatalities for the time period 1984-2003. The main results of this study were (i) The models which we used in order to predict the future risks seem to work satisfactorily. They took very well care of experts who were too certain or uncertain in their assessments causing under- or overestimation of risks. The aggregated models were mostly effected by experts who had less assessment errors and at the same time had the highest confidence, (ii) Calibration of the experts' assessed risks were needed. (iii) We introduced two different methods to estimate the assessment error variances of the experts. The first method was built on probability assessments and the second method on interval assessments. The differences between these two methods were not remarkably prominent. (iv) All individual distributions were positively skewed. While, the aggregated distributions were less skewed.
    A simple sensitivity analysis of the prediction models was performed. The main issues which the sensitivity analysis treated were: (i) how different dependence assumptions affected the predictions, (ii) if the prediction models were influenced more by a certain type of dependence assumption than the other types, and (iii) how the different values of the correlation coefficients affected the predictions. The sensitivity analysiswas built on data from the above mentioned survey. The main results of the sensitivity analysis were: (i) introducing positive and equal correlation coefficients to the prediction models increased the precision of the predictions and (iv) the correlation between the time periods were more essential for the prediction estimations than the correlations concerning the assessments between the groups of experts.

ISBN 91-7153-580-2 

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Last update: 990916/CE