KMS Of Academy of mathematics and systems sciences, CAS
Berry-Esseen bounds for compound-Poisson loss percentiles | |
Feng, Frank Y.1; Powers, Michael R.2; Xiao, Rui'an3; Zhao, Lin4 | |
2017 | |
Source Publication | SCANDINAVIAN ACTUARIAL JOURNAL |
ISSN | 0346-1238 |
Issue | 6Pages:519-534 |
Abstract | The 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. |
Keyword | Berry-Esseen theorem compound-Poisson sums percentile estimation risk theory reinsurance retention |
DOI | 10.1080/03461238.2016.1182064 |
Language | 英语 |
Funding Project | National Science Foundation of China (NSFC)[71301161] ; National Science Foundation of China (NSFC)[71532013] |
WOS Research Area | Mathematics ; Mathematical Methods In Social Sciences |
WOS Subject | Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods ; Statistics & Probability |
WOS ID | WOS:000404263100003 |
Publisher | TAYLOR & FRANCIS LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25877 |
Collection | 系统科学研究所 |
Corresponding Author | Powers, Michael R. |
Affiliation | 1.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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