Regression credibility model with correlation risk under balanced loss function
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摘要: 首先, 给出了平衡损失函数下信度保费估计与二次损失函数下的信度保费估计的关系; 然后, 给出了在平衡损失函数下具有风险相依的回归信度保费表达式; 并讨论了平衡损失函数下, 目标估计为特殊情况的回归信度保费和风险等相关; 以及具有共同效应时, 二种回归信度保费表达式.Abstract: Firstly the relation between the credibility premium under balanced loss function and quadratic loss function was given. Then the linear regression credibility premium with correlation risk under balanced loss function was derived. At last the credibility premium was expressed in balanced loss function when the target estimator was specialized, meanwhile the regression credibility model with equal correlation and common effect risk under balanced loss function was discussed.
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Key words:
- balanced loss function /
- correlation risk /
- regression credibility
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[1] {1}WHITNEY A W. The theory of experience rating[J]. Proceedings of theCasualty Actuarial Society, 1918, 4: 274-292.{2}B\"{U}HLMANN H. Experience rating and credibility [J]. AstinBulletin, 1967, 4: 199-207.{3}B\"{U}HLMANN H, STRAUB E. Glaubw\"{u}rdigkeit f\"{u}r Schaden\"{a}stze[J]. Bulletin Swiss Ass Act, 1967, 70(1): 111-133.{4}JWELL W S. The use of collateral data in credibility theory: ahierarchical model[J]. Giornale dell'Istituto Italiano degliAttuari, 1975, 38: 1-16.{5}HACHEMEISTER C A. Credibility for regression models with applicationto trend[C]//Credibility, Theory and Application: Proeeedings of theBerkeley Actuarial Research Conference on credibility 1975. NewYork: Academic Press, 1975.{6}DHAENE J, DENUIT M, GOOVAERTS M J, et al. The conceptof comonotonicity in actuarial science and finance: theory[J].Insurance: Mathematics and Economics, 2002, 31: 3-33.{7}DHAENE J, DENUIT M, GOOVAERTS M J, et al. The conceptof comonotonicity in actuarial science and finance: applications[J].Insurance: Mathematics and Economics, 2002, 31: 133-161.{8}M\"{U}LLER A. Stop-loss order for portfolios of dependent risks[J].Insurance: Mathematics and Economics, 1997, 21: 219-223.{9}LU T Y, ZHANG Y. Generalized correlation order and stop-lossorder[J]. Insurance: Mathematics and Economics, 2004, 35: 69-76.{10}PURCARU O, DENUIT M. On the dependence induced by frequencycredibility models[J]. Belgian Actuarial Bulletin, 2002, 2(1):73-79.{11}PURCARU O, DENUIT M. Dependence in dynamic claim frequencycredibility models[J]. Astin Bulletin, 2003, 33(1): 23-40.{12}FREES E W, WANG P. Credibility using copulas[J]. North AmericanActuarial Journal, 2005, 9: 31-48.{13}YEO K L, VALDEZ E A. Claim dependence with common effects incredibility models[J]. Insurance: Mathematics and Economics, 2006,38: 609-629.{14}WEN L, WU X, ZHOU X. The credibility premiums for models withdependence induced by common effects[J]. Insurance: Mathematics andEconomics, 2009, 44: 19-25.{15}WEN L, DENG W. The credibility models with equal correlationrisk[J]. J Syst Sci Complex, 2010, 23: 1-8.{16}王筑娟, 温利民. 具有共同效应的信度回归模型[J]. 应用概率统计, 2011,27(3): 312-322.{17}ZELLNER A, GEISEL M S. Sensitivity of Control to Uncertainty andForm of the Criterion Function: The Future of Statistics,269-289[C]. Oshkosh, Wisc: Academia Press, 1968.{18}AITCHISON J, DUNSMORC I R. Statistical Prediction Analysis[M].Cambridge: Cambridge University Press, 1975.{19}ZELLNER A. Bayesian and Non-Bayesian estimation using balanced lossfunctions[C]//Statistical decision theory and Related Topics V. NewYork: Springer-Verlag, 1994: 337-390.{20}RODRIGNES J, ZELLENER A. Weighted balanced loss function andestimation of the mean time to failure[J]. Communications inStatistics Theory and Methods, 1994, 23: 3609-3616.{21}GILES J A, GILES D E A, OHTANI K. The exact risk of some pre-testand Stein-type regression estimators under balanced loss[J].Communications in Statistics-Theory and Methods, 1996, 25:2901-2924.{22}DEY D, GOSH M, STRAWDEEMAN W E. On estimation with balanced lossfunctions[J]. Statist Probab Lett, 1999, 45: 97-101.{23}JOZANI M J, MARCHAND E, PARSIAN A. Bayesian and Robust Bayesiananalysis under a general class of balanced loss functions[J].Statistical Papers, 2012, 53: 51-60.{24}G\'{O}MEZ-D\'{E}NIZ E. A generalization of the credibility theoryobtained by using the weighted balanced loss function[J]. Insurance:Mathematics and Economics, 2008, 42: 850-854.{25}陈希儒, 倪国熙. 数理统计学教程[M]. 上海: 上海科学技术出版社, 1988.{26}温利民. 风险保费的信度估计及其统计推断[D]. 上海:华东师范大学金融与统计学院, 2010.
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