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A new auxiliary function method for systems of nonlinear equations
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 |
References:
[1] |
C. Bolancé, M. Guillén, M. Denuit and J. Pinquet, Bonus-malus scales in segmented tariffs with stochastic migration between segments,, Insurance: Mathematics and Economics, 33 (2003), 273.
doi: 10.1016/S0167-6687(03)00139-2. |
[2] |
H. Bühlmann, Experience rating and credibility,, Astin Bulletin, 4 (1967), 199. Google Scholar |
[3] |
H. Bühlmann and E. Straub, Glaubwüdigkeit für Schadensäze,, Bulletin of the Swiss Association of Actuaries, 70 (1970), 111. Google Scholar |
[4] |
H. Bühlmann and A. Gisler, A Course in Credibility Theory and its Applications,, Springer, (2005). Google Scholar |
[5] |
D. R. Dannenburg, Crossed classification credibility models,, Transactions of the 25th International Congress of Actuaries, 4 (1995), 1. Google Scholar |
[6] |
J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas and D. Vyncke, The concept of comonotonicity in actuarial science and finance: Theory,, Insurance: Mathematics and Economics, 31 (2002), 3.
doi: 10.1016/S0167-6687(02)00134-8. |
[7] |
J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas and D. Vyncke, The concept of comonotonicity in actuarial science and finance: Applications,, Insurance: Mathematics and Economics, 31 (2002), 133.
doi: 10.1016/S0167-6687(02)00135-X. |
[8] |
J. Dhaene and M. J. Goovaerts, Dependency of risks and stop-loss order,, Astin Bulletin, 26 (1996), 201. Google Scholar |
[9] |
E. W. Frees, V. R. Young and Y. Luo, A Longitudinal Date Analysis Interpretation of Credibility models,, Insurance: Mathematics and Economics, 24 (1999), 229.
doi: 10.1016/S0167-6687(98)00055-9. |
[10] |
E. W. Frees, V. R. Young and Y. Luo, Case studies using panel data models,, North American Actuarial Journal, 5 (2001), 24.
doi: 10.1080/10920277.2001.10596010. |
[11] |
C. A. Hachemeister, Credibility for regression models with application to trend,, In Credibility, (1975), 129.
|
[12] |
W. S. Jewell, The use of collateral data in credibility theory: A hierarchical model,, Giorndle dell'lstituto Italianodegdi Attuari, 38 (1975), 1. Google Scholar |
[13] |
T. Y. Lu and Y. Zhang, Generalized correlation order and stop-loss order,, Insurance: mathematics and economics, 35 (2004), 69.
doi: 10.1016/j.insmatheco.2004.04.003. |
[14] |
A. Müller, Stop-loss order for portfolios of dependent risks,, Insurance: Mathematics and Economics, 21 (1997), 219.
doi: 10.1016/S0167-6687(97)00032-2. |
[15] |
M. Pan, R. Wang and X. Wu, On the consistency of credibility premiums regarding Esscher principle,, Insurance: Mathematics and Economics, 42 (2008), 119.
doi: 10.1016/j.insmatheco.2007.01.009. |
[16] |
O. Purcaru and M. Denuit, On the dependence induced by frequency credibility models,, Belgian Actuarial Bulletin, 2 (2002), 73. Google Scholar |
[17] |
O. Purcaru and M. Denuit, Dependence in dynamic claim frequency credibility models,, Astin Bulletin, 33 (2003), 23.
doi: 10.2143/AST.33.1.1037. |
[18] |
S. S. Wang, V. R. Young and H. H. Panjer, Axiomatic characterization of insurance prices,, Insurance: Mathematics and Economics, 21 (1997), 173.
doi: 10.1016/S0167-6687(97)00031-0. |
[19] |
L. Wen, X. Wu and X. Zhao, The credibility premiums under generalized weighted loss functions,, Journal of Industrial and Management Optimization, 5 (2009), 893.
doi: 10.3934/jimo.2009.5.893. |
[20] |
L. Wen, X. Wu and X. Zhou, The credibility premiums for models with dependence induced by common effects,, Insurance: Mathematics and Economics, 44 (2009), 19.
doi: 10.1016/j.insmatheco.2008.09.005. |
[21] |
X. Wu and X. Zhou, A new characterization of distortion premiums via countable additivity for comonotonic risks,, Insurance: Mathematics and Economics, 38 (2006), 324.
doi: 10.1016/j.insmatheco.2005.09.002. |
[22] |
K. L. Yeo and E. A. Valdez, Claim dependence with common effects in credibility models,, Insurance: Mathematics and Economics, 38 (2006), 609.
doi: 10.1016/j.insmatheco.2005.12.006. |
show all references
References:
[1] |
C. Bolancé, M. Guillén, M. Denuit and J. Pinquet, Bonus-malus scales in segmented tariffs with stochastic migration between segments,, Insurance: Mathematics and Economics, 33 (2003), 273.
doi: 10.1016/S0167-6687(03)00139-2. |
[2] |
H. Bühlmann, Experience rating and credibility,, Astin Bulletin, 4 (1967), 199. Google Scholar |
[3] |
H. Bühlmann and E. Straub, Glaubwüdigkeit für Schadensäze,, Bulletin of the Swiss Association of Actuaries, 70 (1970), 111. Google Scholar |
[4] |
H. Bühlmann and A. Gisler, A Course in Credibility Theory and its Applications,, Springer, (2005). Google Scholar |
[5] |
D. R. Dannenburg, Crossed classification credibility models,, Transactions of the 25th International Congress of Actuaries, 4 (1995), 1. Google Scholar |
[6] |
J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas and D. Vyncke, The concept of comonotonicity in actuarial science and finance: Theory,, Insurance: Mathematics and Economics, 31 (2002), 3.
doi: 10.1016/S0167-6687(02)00134-8. |
[7] |
J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas and D. Vyncke, The concept of comonotonicity in actuarial science and finance: Applications,, Insurance: Mathematics and Economics, 31 (2002), 133.
doi: 10.1016/S0167-6687(02)00135-X. |
[8] |
J. Dhaene and M. J. Goovaerts, Dependency of risks and stop-loss order,, Astin Bulletin, 26 (1996), 201. Google Scholar |
[9] |
E. W. Frees, V. R. Young and Y. Luo, A Longitudinal Date Analysis Interpretation of Credibility models,, Insurance: Mathematics and Economics, 24 (1999), 229.
doi: 10.1016/S0167-6687(98)00055-9. |
[10] |
E. W. Frees, V. R. Young and Y. Luo, Case studies using panel data models,, North American Actuarial Journal, 5 (2001), 24.
doi: 10.1080/10920277.2001.10596010. |
[11] |
C. A. Hachemeister, Credibility for regression models with application to trend,, In Credibility, (1975), 129.
|
[12] |
W. S. Jewell, The use of collateral data in credibility theory: A hierarchical model,, Giorndle dell'lstituto Italianodegdi Attuari, 38 (1975), 1. Google Scholar |
[13] |
T. Y. Lu and Y. Zhang, Generalized correlation order and stop-loss order,, Insurance: mathematics and economics, 35 (2004), 69.
doi: 10.1016/j.insmatheco.2004.04.003. |
[14] |
A. Müller, Stop-loss order for portfolios of dependent risks,, Insurance: Mathematics and Economics, 21 (1997), 219.
doi: 10.1016/S0167-6687(97)00032-2. |
[15] |
M. Pan, R. Wang and X. Wu, On the consistency of credibility premiums regarding Esscher principle,, Insurance: Mathematics and Economics, 42 (2008), 119.
doi: 10.1016/j.insmatheco.2007.01.009. |
[16] |
O. Purcaru and M. Denuit, On the dependence induced by frequency credibility models,, Belgian Actuarial Bulletin, 2 (2002), 73. Google Scholar |
[17] |
O. Purcaru and M. Denuit, Dependence in dynamic claim frequency credibility models,, Astin Bulletin, 33 (2003), 23.
doi: 10.2143/AST.33.1.1037. |
[18] |
S. S. Wang, V. R. Young and H. H. Panjer, Axiomatic characterization of insurance prices,, Insurance: Mathematics and Economics, 21 (1997), 173.
doi: 10.1016/S0167-6687(97)00031-0. |
[19] |
L. Wen, X. Wu and X. Zhao, The credibility premiums under generalized weighted loss functions,, Journal of Industrial and Management Optimization, 5 (2009), 893.
doi: 10.3934/jimo.2009.5.893. |
[20] |
L. Wen, X. Wu and X. Zhou, The credibility premiums for models with dependence induced by common effects,, Insurance: Mathematics and Economics, 44 (2009), 19.
doi: 10.1016/j.insmatheco.2008.09.005. |
[21] |
X. Wu and X. Zhou, A new characterization of distortion premiums via countable additivity for comonotonic risks,, Insurance: Mathematics and Economics, 38 (2006), 324.
doi: 10.1016/j.insmatheco.2005.09.002. |
[22] |
K. L. Yeo and E. A. Valdez, Claim dependence with common effects in credibility models,, Insurance: Mathematics and Economics, 38 (2006), 609.
doi: 10.1016/j.insmatheco.2005.12.006. |
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