Fundamentals of Risk Measurement and Aggregation for Insurance Applications
The fundamentals of insurance are introduced and alternatives to risk measurement are presented, illustrating how the size and likelihood of future losses may be quantified. Real data indicate that insurance companies handle many small losses, while large or extreme claims occur only very rarely. The skewness of the profit and loss probability distribution function is especially troublesome for risk quantification, but its strong asymmetry is successfully addressed with generalizations of kernel estimation. Closely connected to this approach, distortion risk measures study the expected losses of a transformation of the original data. GlueVaR risk measures are presented. The notions of subadditivity and tail-subadditivity are discussed and an overview of risk aggregation is given with some additional applications to insurance.
KeywordsRisk analysis Extremes Quantiles Distortion measures
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