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Nonparametric Estimation of Kamp Premium Principle

DOI: 10.12677/SA.2013.23010, PP. 70-75

Keywords: Kamp保费原理;贝叶斯模型;信度估计;收敛性
Kamp Premium Principle
, Bayesian Model, Credibility Estimates, Convergence

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Based on the generalized weighted premium, this paper gives a brief introduction on Kamp pre- mium principle. Through the establishment of Bayesian theory model, a set of samples is given to assume that parameters have a prior distribution. Then the Bayesian formula is used to calculate the posterior mean value. We make Bayesian estimation and linear Bayesian estimation on the Kamp premium principle, and get the credibility estimation of Kamp premium principle after analyzing the approximate of parameters under above conditions. At the same time, we prove the asymptotic of this estimation. Finally, the convergence of the provided estimates is tested by the numerical simulation.


[1]  W. R. Heilmann. Decision theoretic foundations of credibility theory. Insurance: Mathematics and Economics, 1989, 8: 77-95.
[2]  H. U. Gerber. An introduction to Mathematical risk theory. Phi- ladelphia: S.S. Heubner Foundation, 1979: Monograph Series 8.
[3]  H. U. Gerber. Credibility for Esscher premium. Bulletin of the Swiss Asso-ciation of Actuaries, 1980, 3: 307-312.
[4]  E. Furman, R. Zitikis. Weighted premium calculation principles. Insurance: Mathematics and Economics, 2008, 42(1): 459-465.
[5]  W. Herff, B. Jochems and U. Kamps. The inspection paradox with random time. Statistical Papers, 1997, 38: 103-110.
[6]  U. Kamps. On a class of premium principles including the Ess- cher principle. Scandinavian Actuarial Journal, 1998, 1: 75-80.
[7]  K. D. Schmidt, M. Timpel. Experience rating under weighted squared error loss. Bl?tter der DGVFM, 1995, 22(2): 289-307.
[8]  M. Pan, R. Wang, and X. Wu. On the consistency of credibility premiums regarding Esscher principle. Insurance: Mathe-matics and Economics, 2008, 42: 119-126.
[9]  D. Vylder. Estimation of IBNR claims by credibility theory. Insurance: Mathematics and Economics, 1982, 1:35-40.
[10]  温利民,风险保费的信度估计及其统计推断[J]. 华东师范大学学报, 2010, 3: 103-270.
[11]  王伟等. Esscher保费原理下信度估计的比较[J]. 华东师范大学学报, 2010, 3: 71-78.
[12]  L. Wen, X. Wu and X. Zhao. The credibility premiums under generalized weighted loss functions. Journal of Industrial and Management Optimization, 2009, 5(4): 893-910.
[13]  G. Shorack, J. Wellner. Empirical processes with applications to statistics. New York: Wiley, 1986.
[14]  Y. J. Kim. Credibility theory based on trimming. Insurance: Ma- thematics and Economics. 2013, 53: 36-47.


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