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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), 273-282.
doi: 10.1016/S0167-6687(03)00139-2. |
[2] |
H. Bühlmann, Experience rating and credibility, Astin Bulletin, 4 (1967), 199-207. |
[3] |
H. Bühlmann and E. Straub, Glaubwüdigkeit für Schadensäze, Bulletin of the Swiss Association of Actuaries, 70 (1970), 111-133. |
[4] |
H. Bühlmann and A. Gisler, A Course in Credibility Theory and its Applications, Springer, Netherlands, 2005. |
[5] |
D. R. Dannenburg, Crossed classification credibility models, Transactions of the 25th International Congress of Actuaries, 4 (1995), 1-35. |
[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), 3-33.
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), 133-161.
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), 201-212. |
[9] |
E. W. Frees, V. R. Young and Y. Luo, A Longitudinal Date Analysis Interpretation of Credibility models, Insurance: Mathematics and Economics, 24 (1999), 229-247.
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), 24-42.
doi: 10.1080/10920277.2001.10596010. |
[11] |
C. A. Hachemeister, Credibility for regression models with application to trend, In Credibility, theory and application. Proceedings of the Berkeley Actuarial Research Conference on credibility, Academic Press, New York, (1975), 129-169. |
[12] |
W. S. Jewell, The use of collateral data in credibility theory: A hierarchical model, Giorndle dell'lstituto Italianodegdi Attuari, 38 (1975), 1-16. |
[13] |
T. Y. Lu and Y. Zhang, Generalized correlation order and stop-loss order, Insurance: mathematics and economics, 35 (2004), 69-76.
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), 219-223.
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), 119-126.
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), 73-79. |
[17] |
O. Purcaru and M. Denuit, Dependence in dynamic claim frequency credibility models, Astin Bulletin, 33 (2003), 23-40.
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), 173-183.
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), 893-910.
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), 19-25.
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), 324-334.
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), 609-629.
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), 273-282.
doi: 10.1016/S0167-6687(03)00139-2. |
[2] |
H. Bühlmann, Experience rating and credibility, Astin Bulletin, 4 (1967), 199-207. |
[3] |
H. Bühlmann and E. Straub, Glaubwüdigkeit für Schadensäze, Bulletin of the Swiss Association of Actuaries, 70 (1970), 111-133. |
[4] |
H. Bühlmann and A. Gisler, A Course in Credibility Theory and its Applications, Springer, Netherlands, 2005. |
[5] |
D. R. Dannenburg, Crossed classification credibility models, Transactions of the 25th International Congress of Actuaries, 4 (1995), 1-35. |
[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), 3-33.
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), 133-161.
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), 201-212. |
[9] |
E. W. Frees, V. R. Young and Y. Luo, A Longitudinal Date Analysis Interpretation of Credibility models, Insurance: Mathematics and Economics, 24 (1999), 229-247.
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), 24-42.
doi: 10.1080/10920277.2001.10596010. |
[11] |
C. A. Hachemeister, Credibility for regression models with application to trend, In Credibility, theory and application. Proceedings of the Berkeley Actuarial Research Conference on credibility, Academic Press, New York, (1975), 129-169. |
[12] |
W. S. Jewell, The use of collateral data in credibility theory: A hierarchical model, Giorndle dell'lstituto Italianodegdi Attuari, 38 (1975), 1-16. |
[13] |
T. Y. Lu and Y. Zhang, Generalized correlation order and stop-loss order, Insurance: mathematics and economics, 35 (2004), 69-76.
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), 219-223.
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), 119-126.
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), 73-79. |
[17] |
O. Purcaru and M. Denuit, Dependence in dynamic claim frequency credibility models, Astin Bulletin, 33 (2003), 23-40.
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), 173-183.
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), 893-910.
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), 19-25.
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), 324-334.
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), 609-629.
doi: 10.1016/j.insmatheco.2005.12.006. |
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