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On weighted balanced loss function under the Esscher principle and credibility premiums

Yıl 2018, Cilt: 47 Sayı: 1, 255 - 265, 01.02.2018

Öz

This paper focuses on weighted balanced loss function under the Esscher principle (WBLF) of which we explore the modern practice of credibility theory and we generalize credibility premiums by using the WBLF. We obtain a distribution-free approach under the WBLF and the Esscher premium by using a minimization technique. Also, we discuss the consistency of the credibility premium generated by this distribution-free approach.

Kaynakça

  • Bühlmann, H. Experience rating and credibility, Astin Bulletin 4, 199-207, 1967.
  • Bühlmann, H., Gisler, A. A Course in Credibility Theory and its Applications, Springer, Netherlands, 2005.
  • Dey, D.G., Ghosh, M., Strawderman, W. On estimation with balanced loss functions, Sta- tistics and Probability Letters 45, 97-101, 1999.
  • Farsipour, N.S., Asgharzadhe, A. Estimation of a normal mean relative to balanced loss functions, Statistical Papers 45, 279-286, 2004.
  • Gómez Déniz. On the use of the weighted balanced loss function to obtain credibility premi- ums, International conference on mathematical and statistical modeling in Honor of Enrique Castillo, June 28-30, 2006.
  • Gómez Déniz. A generalization of the credibility theory obtained by using the weighted bal- anced loss function, Insurance: Mathematics and Economics 42, 850-854, 2008.
  • Goovaerts, M.J., De Vylder.F. and Haezendonck. J. Insurance Premiums: Theory and Ap- plications. North-Holland. Amsterdam, 1984.
  • Goovaerts, M.J. and Hoogstad, W.J. Credibility Theory. In: Surveys of Actuarial Studies, 4, Nationale-Nederlanden N.V., Rotterdam, 1987.
  • Gupta, S. and Berger, J. Statistical Decision Theory and Related Topics, Springer, New York, 371-390, 1994.
  • Heilmann, W. Decision theoretic foundations of credibility theory, Insurance: Mathematics and Economics 8 (1), 77-95, 1989.
  • Herzog, T.N. Introduction to Credibility Theory, 2nd edition, ACTEX Publications, Win- sted, 1996.
  • Jafari, M., Marchand, E., Parsian, A. On estimation with weighted balanced-type loss func- tion, Statistics and Probability Letters 76, 773-780, 2006.
  • Kaas, R., Dannenburg, D., Goovaerts, M. Exact credibility for weighted observations, Astin Bulletin 27 (2), 287-295, 1996.
  • Klugman, S.A., Panjer, H.H., Willmot, G.E. Loss Models: From Data to Decisions, John Wiley and Sons, New York, 2004.
  • Maolin Pan, Rongming Wang, Xianyi Wu. On the consistency of credibility premiums re- garding Esscher principle, Insurance: Mathematics and Economics 42, 119-126, 2008.
  • Najafabadi, Amir T. Payandeh. A new approach to the credibility formula, Insurance: Math- ematics and Economics 46, 334-338, 2010.
  • Norberg, R. Credibility theory. In: Encyclopedia of Actuarial Science, Wiley, Chichester, UK, 2004.
  • Rodermund, M. Introduction, Foundations of Casualty Actuarial Science, Chapter 1. New York: Casualty Actuarial Society, 1989.
  • Van Heerwaarden. A.E., Kaas, R. and Goovaerts, M.J. Optimal reinsurance in relation to ordering of risks, Insurance: Mathematics and Economics 8. (1), 11-17, 1989.
  • Zellner, A. Bayesian and non-Bayesian estimation using balanced loss function, In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390, 1994.
Yıl 2018, Cilt: 47 Sayı: 1, 255 - 265, 01.02.2018

Öz

Kaynakça

  • Bühlmann, H. Experience rating and credibility, Astin Bulletin 4, 199-207, 1967.
  • Bühlmann, H., Gisler, A. A Course in Credibility Theory and its Applications, Springer, Netherlands, 2005.
  • Dey, D.G., Ghosh, M., Strawderman, W. On estimation with balanced loss functions, Sta- tistics and Probability Letters 45, 97-101, 1999.
  • Farsipour, N.S., Asgharzadhe, A. Estimation of a normal mean relative to balanced loss functions, Statistical Papers 45, 279-286, 2004.
  • Gómez Déniz. On the use of the weighted balanced loss function to obtain credibility premi- ums, International conference on mathematical and statistical modeling in Honor of Enrique Castillo, June 28-30, 2006.
  • Gómez Déniz. A generalization of the credibility theory obtained by using the weighted bal- anced loss function, Insurance: Mathematics and Economics 42, 850-854, 2008.
  • Goovaerts, M.J., De Vylder.F. and Haezendonck. J. Insurance Premiums: Theory and Ap- plications. North-Holland. Amsterdam, 1984.
  • Goovaerts, M.J. and Hoogstad, W.J. Credibility Theory. In: Surveys of Actuarial Studies, 4, Nationale-Nederlanden N.V., Rotterdam, 1987.
  • Gupta, S. and Berger, J. Statistical Decision Theory and Related Topics, Springer, New York, 371-390, 1994.
  • Heilmann, W. Decision theoretic foundations of credibility theory, Insurance: Mathematics and Economics 8 (1), 77-95, 1989.
  • Herzog, T.N. Introduction to Credibility Theory, 2nd edition, ACTEX Publications, Win- sted, 1996.
  • Jafari, M., Marchand, E., Parsian, A. On estimation with weighted balanced-type loss func- tion, Statistics and Probability Letters 76, 773-780, 2006.
  • Kaas, R., Dannenburg, D., Goovaerts, M. Exact credibility for weighted observations, Astin Bulletin 27 (2), 287-295, 1996.
  • Klugman, S.A., Panjer, H.H., Willmot, G.E. Loss Models: From Data to Decisions, John Wiley and Sons, New York, 2004.
  • Maolin Pan, Rongming Wang, Xianyi Wu. On the consistency of credibility premiums re- garding Esscher principle, Insurance: Mathematics and Economics 42, 119-126, 2008.
  • Najafabadi, Amir T. Payandeh. A new approach to the credibility formula, Insurance: Math- ematics and Economics 46, 334-338, 2010.
  • Norberg, R. Credibility theory. In: Encyclopedia of Actuarial Science, Wiley, Chichester, UK, 2004.
  • Rodermund, M. Introduction, Foundations of Casualty Actuarial Science, Chapter 1. New York: Casualty Actuarial Society, 1989.
  • Van Heerwaarden. A.E., Kaas, R. and Goovaerts, M.J. Optimal reinsurance in relation to ordering of risks, Insurance: Mathematics and Economics 8. (1), 11-17, 1989.
  • Zellner, A. Bayesian and non-Bayesian estimation using balanced loss function, In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371-390, 1994.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm İstatistik
Yazarlar

Farouk Metiri Bu kişi benim

Halim Zeghdoudi Bu kişi benim

Mohamed Riad Remita Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 1

Kaynak Göster

APA Metiri, F., Zeghdoudi, H., & Remita, M. R. (2018). On weighted balanced loss function under the Esscher principle and credibility premiums. Hacettepe Journal of Mathematics and Statistics, 47(1), 255-265.
AMA Metiri F, Zeghdoudi H, Remita MR. On weighted balanced loss function under the Esscher principle and credibility premiums. Hacettepe Journal of Mathematics and Statistics. Şubat 2018;47(1):255-265.
Chicago Metiri, Farouk, Halim Zeghdoudi, ve Mohamed Riad Remita. “On Weighted Balanced Loss Function under the Esscher Principle and Credibility Premiums”. Hacettepe Journal of Mathematics and Statistics 47, sy. 1 (Şubat 2018): 255-65.
EndNote Metiri F, Zeghdoudi H, Remita MR (01 Şubat 2018) On weighted balanced loss function under the Esscher principle and credibility premiums. Hacettepe Journal of Mathematics and Statistics 47 1 255–265.
IEEE F. Metiri, H. Zeghdoudi, ve M. R. Remita, “On weighted balanced loss function under the Esscher principle and credibility premiums”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 1, ss. 255–265, 2018.
ISNAD Metiri, Farouk vd. “On Weighted Balanced Loss Function under the Esscher Principle and Credibility Premiums”. Hacettepe Journal of Mathematics and Statistics 47/1 (Şubat 2018), 255-265.
JAMA Metiri F, Zeghdoudi H, Remita MR. On weighted balanced loss function under the Esscher principle and credibility premiums. Hacettepe Journal of Mathematics and Statistics. 2018;47:255–265.
MLA Metiri, Farouk vd. “On Weighted Balanced Loss Function under the Esscher Principle and Credibility Premiums”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 1, 2018, ss. 255-6.
Vancouver Metiri F, Zeghdoudi H, Remita MR. On weighted balanced loss function under the Esscher principle and credibility premiums. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):255-6.