American Institute of Mathematical Sciences

April  2015, 11(2): 365-380. doi: 10.3934/jimo.2015.11.365

Credibility models with dependence structure over risks and time horizon

 1 Department of Mathematics, Shanghai Maritime University, Shanghai, China 2 Center of International Finance and Risk Management, Department of Statistics and Actuarial Science, East China Normal University, Shanghai, China

Received  November 2012 Revised  March 2014 Published  September 2014

In this paper, the Bühlmann and Bühlmann-Straub's credibility models with a type of dependence structures over risks and over time are discussed. The inhomogeneous and homogeneous credibility estimators of risk premium were derived. The inhomogeneous credibility estimators for the existing credibility models with common effects are extended to slightly more general versions. The results obtained shake the classical meaning of the term credibility premiums''.
Citation: Weizhong Huang, Xianyi Wu. Credibility models with dependence structure over risks and time horizon. Journal of Industrial & Management Optimization, 2015, 11 (2) : 365-380. doi: 10.3934/jimo.2015.11.365
References:

show all references

References:
 [1] Qiang Zhang, Ping Chen. Multidimensional balanced credibility model with time effect and two level random common effects. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019004 [2] 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 [3] Ke Ruan, Masao Fukushima. Robust portfolio selection with a combined WCVaR and factor model. Journal of Industrial & Management Optimization, 2012, 8 (2) : 343-362. doi: 10.3934/jimo.2012.8.343 [4] Shaoyong Lai, Yulan Zhou. A stochastic optimal growth model with a depreciation factor. Journal of Industrial & Management Optimization, 2010, 6 (2) : 283-297. doi: 10.3934/jimo.2010.6.283 [5] Justin P. Peters, Khalid Boushaba, Marit Nilsen-Hamilton. A Mathematical Model for Fibroblast Growth Factor Competition Based on Enzyme. Mathematical Biosciences & Engineering, 2005, 2 (4) : 789-810. doi: 10.3934/mbe.2005.2.789 [6] Ruijun Zhao, Yong-Tao Zhang, Shanqin Chen. Krylov implicit integration factor WENO method for SIR model with directed diffusion. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4983-5001. doi: 10.3934/dcdsb.2019041 [7] Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi. Mathematical analysis of a HIV model with frequency dependence and viral diversity. Mathematical Biosciences & Engineering, 2008, 5 (3) : 457-476. doi: 10.3934/mbe.2008.5.457 [8] Xiaoming Zheng, Gou Young Koh, Trachette Jackson. A continuous model of angiogenesis: Initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1109-1154. doi: 10.3934/dcdsb.2013.18.1109 [9] Mostafa Adimy, Fabien Crauste. Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 19-38. doi: 10.3934/dcdsb.2007.8.19 [10] Mohammad-Sahadet Hossain. Projection-based model reduction for time-varying descriptor systems: New results. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 73-90. doi: 10.3934/naco.2016.6.73 [11] Roland Pulch. Stability preservation in Galerkin-type projection-based model order reduction. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 23-44. doi: 10.3934/naco.2019003 [12] Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105 [13] Jiangyan Peng, Dingcheng Wang. Asymptotics for ruin probabilities of a non-standard renewal risk model with dependence structures and exponential Lévy process investment returns. Journal of Industrial & Management Optimization, 2017, 13 (1) : 155-185. doi: 10.3934/jimo.2016010 [14] Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42. [15] K. T. Arasu, Manil T. Mohan. Optimization problems with orthogonal matrix constraints. Numerical Algebra, Control & Optimization, 2018, 8 (4) : 413-440. doi: 10.3934/naco.2018026 [16] Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial & Management Optimization, 2006, 2 (4) : 451-466. doi: 10.3934/jimo.2006.2.451 [17] Yinghui Dong, Guojing Wang. The dependence of assets and default threshold with thinning-dependence structure. Journal of Industrial & Management Optimization, 2012, 8 (2) : 391-410. doi: 10.3934/jimo.2012.8.391 [18] Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135 [19] Ryusuke Kon. Dynamics of competitive systems with a single common limiting factor. Mathematical Biosciences & Engineering, 2015, 12 (1) : 71-81. doi: 10.3934/mbe.2015.12.71 [20] Yanming Ge. Analysis of airline seat control with region factor. Journal of Industrial & Management Optimization, 2012, 8 (2) : 363-378. doi: 10.3934/jimo.2012.8.363

2018 Impact Factor: 1.025