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- Rootzen, Holger, 1945, et al.
(författare)
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Univariate and Bivariate GPD Methods for Predicting Extreme Wind Storm Losses
- 2009
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Ingår i: Insurance: Mathematics and Economics. - : Elsevier BV. - 0167-6687. ; 44:2, s. 345-356
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 4. |
- Brodin, Erik, 1975
(författare)
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Extreme Value Statistics and Quantile Estimation with Applications in Finance and Insurance
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis presents results in Extreme Value Statistics and quantile estimation. A first part includes a popular scientific introduction to Extreme Value Statistics and a review paper on Extreme Value Theory in finance. Further, we study new non-parametric quantile estimators for non-extreme quantiles. After concluding that these have the same asymptotic distribution as sample quantiles, a simulation study shows that their small sample performance is better in many cases than that of the sample quantile. In the part of this thesis dealing with finance we study extreme dependence between stock market log returns sampled at different frequencies using the so-called tail dependence function. We also investigate the "stylized fact" that log returns have Semi-heavy tails. The next topic is insurance losses resulting from wind storm damages in southern Sweden. A detailed statistical analysis detects a weak trend, that non-extreme quantiles of individual storms increase with time, but no other trends. We also find prediction intervals for the sizes of future storm losses using both a univariate and a bivariate model. One conclusion is that the major Swedish storm Gudrun was not unlikely to occur. Finally, we introduce the models used in the insurance application into risk management in finance.
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| 5. |
- Brodin, Erik, 1975
(författare)
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On quantile estimation by bootstrap
- 2006
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Ingår i: Computational Statistics and Data Analysis. - : Elsevier BV. - 0167-9473. ; 50:6, s. 1398-1406
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Tidskriftsartikel (refereegranskat)abstract
- Exact bootstrap is used to optimize the weights of an L-estimator for quantiles with respect to the estimated MSE (mean square error). Performance of the new estimator is measured by comparing MSE with the sample quantile. The new estimator performs better than the sample quantiles in almost every case. However, the gain is only about 5%, in terms of decreased MSE.
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