American Institute of Mathematical Sciences

Advanced
October  2009, 5(4): 893-910. doi: 10.3934/jimo.2009.5.893

The credibility premiums under generalized weighted loss functions

Limin Wen 1, , Xianyi Wu 1, and  Xiaobing Zhao 2,

1. 

Department of Statistics and Actuarial Science, East China Normal University, Shanghai, China, China
2. 

School of Science, Jiangnan University, Wuxi, Jiangsu, China

Received  August 2008 Revised  March 2009 Published  August 2009

In the classical credibility theory, almost all the credibility premium models are built on the basis of pure premium. However, the insurance practice demands that the premium must have a positive safety loading. In this paper, we consider the premium principle induced by a generalized loss function that can provide the premium principle with\ a positive safety loading. Under this generalized loss function, we derive its Bayes premium and two types of credibility premiums. Both credibility premiums are approximately convex combinations of the collective premium and some functions of the historical claims; while in a first case the function is linear in the historical claims and the corresponding credibility premium is not consistency, in the other one the function is taken as an empirical version of the individual premium and the corresponding credibility premium converges to the individual premium.
Keywords: safety loading., generalized weighted premium, credibility estimator, generalized weighted loss function, consistency.
Mathematics Subject Classification: Primary: 91B30, 62P05; Secondary: 91B8.
Citation: Limin Wen, Xianyi Wu, Xiaobing Zhao. The credibility premiums under generalized weighted loss functions. Journal of Industrial & Management Optimization, 2009, 5 (4) : 893-910. doi: 10.3934/jimo.2009.5.893
[1]

Huiying Fan, Tao Ma. Parabolic equations involving Laguerre operators and weighted mixed-norm estimates. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5487-5508. doi: 10.3934/cpaa.2020249
[2]

Anna Abbatiello, Eduard Feireisl, Antoní Novotný. Generalized solutions to models of compressible viscous fluids. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 1-28. doi: 10.3934/dcds.2020345
[3]

Qianqian Han, Xiao-Song Yang. Qualitative analysis of a generalized Nosé-Hoover oscillator. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020346
[4]

Anna Canale, Francesco Pappalardo, Ciro Tarantino. Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020274
[5]

Shun Zhang, Jianlin Jiang, Su Zhang, Yibing Lv, Yuzhen Guo. ADMM-type methods for generalized multi-facility Weber problem. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020171
[6]

Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020469
[7]

Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020319
[8]

Aihua Fan, Jörg Schmeling, Weixiao Shen. $ L^\infty $-estimation of generalized Thue-Morse trigonometric polynomials and ergodic maximization. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 297-327. doi: 10.3934/dcds.2020363
[9]

Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020445
[10]

Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020  doi: 10.3934/fods.2020018
[11]

Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296
[12]

Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013
[13]

Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020443
[14]

Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070
[15]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (40)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences