基于中国地震的损失模型(英文)
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摘要
对损失分布的估计一直是保险公司的重要问题. 有多种参数方法以及非参数方法拟合损失分布. 本文作者提出了结合参数和非参数的方法来解决损失分布拟合问题. 首先通过超额均值图确定大小损失之间的阈限,再利用广义Pareto分布拟合阈值以上损失, 转换后的核密度估计拟合阈值以下损失. 最后, 通过实证分析将该方法和其他方法进行了误差分析比较, 取得了理想的结果.
The estimation of loss distribution is always a big issue for insurance companies.Several parametric or nonparametric methods are introduced to fit loss distributions.In this paper,we propose a method by combining both parametric and nonparametric methods to solve this problem.We first determine the threshold between large and small losses by observing the graph of mean excess function,then use the generalized Pareto distribution,the parametric method,to fit excess data,and use kernel density estimation,the nonparametric method,to fit the distribution below threshold.Finally,we use a data set about Chinese annual earthquake loss to compare this method with other existing methods.
The estimation of loss distribution is always a big issue for insurance companies.Several parametric or nonparametric methods are introduced to fit loss distributions.In this paper,we propose a method by combining both parametric and nonparametric methods to solve this problem.We first determine the threshold between large and small losses by observing the graph of mean excess function,then use the generalized Pareto distribution,the parametric method,to fit excess data,and use kernel density estimation,the nonparametric method,to fit the distribution below threshold.Finally,we use a data set about Chinese annual earthquake loss to compare this method with other existing methods.
引文
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[2] Wand,M.P.,Marron,J.S. and Ruppert,D.,Transformations in density estimation,Journal of the American Statistical Association,86(1991),343-353.
[3] Bolancé,C.,Guillén,M. and Nielsen,J.P.,Kernel density estimation of actuarial loss functions, Insurance: Mathematics and Economics,32(2003),19-36.
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[2] Wand,M.P.,Marron,J.S. and Ruppert,D.,Transformations in density estimation,Journal of the American Statistical Association,86(1991),343-353.
[3] Bolancé,C.,Guillén,M. and Nielsen,J.P.,Kernel density estimation of actuarial loss functions, Insurance: Mathematics and Economics,32(2003),19-36.
[4] Clements,A.,Hurn,S. and Lindsay,K.,Mobius-like mappings and their use in kernel density esti- mation,Journal of the American Statistical Association,98(2003),993-1000.
[5] Buch-Larsen,T.,Nielsen,J.P.,Guillén,M. and Bolancé,C.,Kernel density estimation for heavy- tailed distributions using the Champernowne transformation,Statistics,39(6)(2005),503-518.
[6] Beirlant,J. and Teugels,J.L.,Modeling large claims in non-life insurance,Insurance: Mathematics and Economics,11(1992),17-29.
[7] Embrechts,P. and Kluppelberg,C.,Some aspects of insurance mathematics,Theory of Probability and Its Applications,38(1993),262-295.
[8] Rootzén,H. and Tajvidi,N.,Extreme value statistics and wind storm losses: a case study,Scandi- navian Actuarial Journal,1(1997),70-94.
[9] McNeil,A.J. and Saladin,T.,The peaks over thresholds method for estimating high quantiles of loss distributions,Proceedings of XXVIIth International Astin Colloquium,1997,23-43.
[10] Hall,P. and Marron,J.S.,Estimation of integrated squared density derivatives,Statistics & Probability Letters,6(1987),100-115.
[11] Silverman,B.W.,Density Estimation for Statistics and Data Analysis,Chapman & Hall,1986.
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