# American Institute of Mathematical Sciences

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

## The credibility premiums under generalized weighted loss functions

 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.
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] Jin-Cheng Jiang, Chengbo Wang, Xin Yu. Generalized and weighted Strichartz estimates. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1723-1752. doi: 10.3934/cpaa.2012.11.1723 [2] Imre Csiszar and Paul C. Shields. Consistency of the BIC order estimator. Electronic Research Announcements, 1999, 5: 123-127. [3] Lee DeVille, Nicole Riemer, Matthew West. Convergence of a generalized Weighted Flow Algorithm for stochastic particle coagulation. Journal of Computational Dynamics, 2019, 6 (1) : 69-94. doi: 10.3934/jcd.2019003 [4] Shouming Zhou. The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4967-4986. doi: 10.3934/dcds.2014.34.4967 [5] Qichun Wang, Chik How Tan, Pantelimon Stănică. Concatenations of the hidden weighted bit function and their cryptographic properties. Advances in Mathematics of Communications, 2014, 8 (2) : 153-165. doi: 10.3934/amc.2014.8.153 [6] Seung Jun Chang, Jae Gil Choi. Generalized transforms and generalized convolution products associated with Gaussian paths on function space. Communications on Pure & Applied Analysis, 2020, 19 (1) : 371-389. doi: 10.3934/cpaa.2020019 [7] Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091 [8] Ana-Maria Acu, Laura Hodis, Ioan Rasa. Multivariate weighted kantorovich operators. Mathematical Foundations of Computing, 2020, 3 (2) : 117-124. doi: 10.3934/mfc.2020009 [9] Sean Holman, Plamen Stefanov. The weighted Doppler transform. Inverse Problems & Imaging, 2010, 4 (1) : 111-130. doi: 10.3934/ipi.2010.4.111 [10] Kanji Inui, Hikaru Okada, Hiroki Sumi. The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions. Discrete & Continuous Dynamical Systems - A, 2020, 40 (2) : 753-766. doi: 10.3934/dcds.2020060 [11] Simon Gindikin. A remark on the weighted Radon transform on the plane. Inverse Problems & Imaging, 2010, 4 (4) : 649-653. doi: 10.3934/ipi.2010.4.649 [12] Tim McGraw, Baba Vemuri, Evren Özarslan, Yunmei Chen, Thomas Mareci. Variational denoising of diffusion weighted MRI. Inverse Problems & Imaging, 2009, 3 (4) : 625-648. doi: 10.3934/ipi.2009.3.625 [13] Ronan Costaouec, Haoyun Feng, Jesús Izaguirre, Eric Darve. Analysis of the accelerated weighted ensemble methodology. Conference Publications, 2013, 2013 (special) : 171-181. doi: 10.3934/proc.2013.2013.171 [14] Igor E. Pritsker and Richard S. Varga. Weighted polynomial approximation in the complex plane. Electronic Research Announcements, 1997, 3: 38-44. [15] Tahar Z. Boulmezaoud, Amel Kourta. Some identities on weighted Sobolev spaces. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 427-434. doi: 10.3934/dcdss.2012.5.427 [16] Yu-Lin Chang, Jein-Shan Chen, Jia Wu. Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function. Journal of Industrial & Management Optimization, 2013, 9 (1) : 153-169. doi: 10.3934/jimo.2013.9.153 [17] Miaohua Jiang. Derivative formula of the potential function for generalized SRB measures of hyperbolic systems of codimension one. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 967-983. doi: 10.3934/dcds.2015.35.967 [18] Raffaela Capitanelli, Maria Agostina Vivaldi. Uniform weighted estimates on pre-fractal domains. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1969-1985. doi: 10.3934/dcdsb.2014.19.1969 [19] Daniel Mckenzie, Steven Damelin. Power weighted shortest paths for clustering Euclidean data. Foundations of Data Science, 2019, 1 (3) : 307-327. doi: 10.3934/fods.2019014 [20] Claudia Anedda, Giovanni Porru. Boundary estimates for solutions of weighted semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3801-3817. doi: 10.3934/dcds.2012.32.3801

2019 Impact Factor: 1.366