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Berry-Esseen bounds for compound-Poisson loss percentiles
Feng, Frank Y.1; Powers, Michael R.2; Xiao, Rui'an3; Zhao, Lin4
AbstractThe Berry-Esseen (BE) theorem of probability theory is employed to establish bounds on percentile estimates for compound-Poisson loss portfolios. We begin by arguing that these bounds should not be based upon the exact BE constant, but rather upon a possibly lower, asymptotic counterpart for which the Lyapunov fraction converges uniformly to zero. We use this constant to construct two bounds - one approximate, and the other exact - and then propose a simple numerical criterion for determining whether the Gaussian approximation affords sufficient accuracy for a given Poisson mean and individual-loss distribution. Applying this criterion to the cases of gamma and lognormal individual losses, we find there exists a positive lower bound for the minimum Poisson mean necessary to achieve a fixed degree of accuracy for losses generated by the best-case' individual-loss distribution. Further investigation of this best case' reveals that large minimum Poisson means (i.e. >700) are required to achieve reasonable accuracy for the 99th percentile associated with these losses. Finally, we consider how the upper BE bound of a tail percentile may be applied to a common practical problem: selecting excess-of-loss reinsurance retentions.
KeywordBerry-Esseen theorem compound-Poisson sums percentile estimation risk theory reinsurance retention
Funding ProjectNational Science Foundation of China (NSFC)[71301161] ; National Science Foundation of China (NSFC)[71532013]
WOS Research AreaMathematics ; Mathematical Methods In Social Sciences
WOS SubjectMathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods ; Statistics & Probability
WOS IDWOS:000404263100003
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Document Type期刊论文
Corresponding AuthorPowers, Michael R.
Affiliation1.Tsinghua Univ, China Ctr Insurance & Risk Management, Sch Econ & Management, Beijing, Peoples R China
2.Tsinghua Univ, Sch Econ & Management, Dept Finance, Beijing, Peoples R China
3.NYU, Grad Sch Arts & Sci, New York, NY USA
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Feng, Frank Y.,Powers, Michael R.,Xiao, Rui'an,et al. Berry-Esseen bounds for compound-Poisson loss percentiles[J]. SCANDINAVIAN ACTUARIAL JOURNAL,2017(6):519-534.
APA Feng, Frank Y.,Powers, Michael R.,Xiao, Rui'an,&Zhao, Lin.(2017).Berry-Esseen bounds for compound-Poisson loss percentiles.SCANDINAVIAN ACTUARIAL JOURNAL(6),519-534.
MLA Feng, Frank Y.,et al."Berry-Esseen bounds for compound-Poisson loss percentiles".SCANDINAVIAN ACTUARIAL JOURNAL .6(2017):519-534.
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