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Univariate and Bivariate GPD Methods for Predicting Extreme Wind Storm Losses

Artikel i vetenskaplig tidskrift
Författare Holger Rootzén
Erik Brodin
Publicerad i Insurance: Mathematics and Economics
Volym 44
Nummer/häfte 2
Sidor 345-356
ISSN 0167-6687
Publiceringsår 2009
Publicerad vid Institutionen för matematiska vetenskaper, matematisk statistik
Sidor 345-356
Språk en
Länkar www.sciencedirect.com/science?_ob=A...
Ämnesord Extreme value statistics; Generalized Pareto distribution; Likelihood prediction intervals; Peaks over threshold; Trend analysis; Wind storm losses
Ämneskategorier Tillämpad matematik, Annan matematik

Sammanfattning

Wind storm and hurricane risks are attracting increased attention as a result of recent catastrophic events. The aim of this paper is to select, tailor, and develop extreme value methods for use in wind storm insurance. The methods are applied to the 1982–2005 losses for the largest Swedish insurance company, the Länsförsäkringar group. Both a univariate and a new bivariate Generalized Pareto Distribution (GPD) gave models which fitted the data well. The bivariate model led to lower estimates of risk, except for extreme cases, but taking statistical uncertainty into account the two models lead to qualitatively similar results. We believe that the bivariate model provided the most realistic picture of the real uncertainties. It additionally made it possible to explore the effects of changes in the insurance portfolio, and showed that loss distributions are rather insensitive to portfolio changes. We found a small trend in the sizes of small individual claims, but no other trends. Finally, we believe that companies should develop systematic ways of thinking about “not yet seen” disasters.

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