Geodesic
The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts
Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 389-405

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
This paper presents and analyzes the estimators of the structural parameters, in the Bühlmann-Straub model, involving complicated mathematical properties of conditional expectations and of conditional covariances. So to enable to use the better linear credibility results obtained in this model, we will provide useful estimators for the structure parameters. From the practical point of view it is stated the attractive property of unbiasedness for these estimators.
This paper presents and analyzes the estimators of the structural parameters, in the Bühlmann-Straub model, involving complicated mathematical properties of conditional expectations and of conditional covariances. So to enable to use the better linear credibility results obtained in this model, we will provide useful estimators for the structure parameters. From the practical point of view it is stated the attractive property of unbiasedness for these estimators.
DOI : 10.21136/MB.2007.133964
Classification : 62F10, 62P05, 91B30
Keywords: credibility premium; structure parameters; unbiased estimators; Bühlmann-Straub model 
Atanasiu, Virginia. The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts. Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 389-405. doi: 10.21136/MB.2007.133964
@article{10_21136_MB_2007_133964,
     author = {Atanasiu, Virginia},
     title = {The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts},
     journal = {Mathematica Bohemica},
     pages = {389--405},
     year = {2007},
     volume = {132},
     number = {4},
     doi = {10.21136/MB.2007.133964},
     mrnumber = {2365323},
     zbl = {1174.62547},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.133964/}
}
TY  - JOUR
AU  - Atanasiu, Virginia
TI  - The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts
JO  - Mathematica Bohemica
PY  - 2007
SP  - 389
EP  - 405
VL  - 132
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.133964/
DO  - 10.21136/MB.2007.133964
LA  - en
ID  - 10_21136_MB_2007_133964
ER  - 
%0 Journal Article
%A Atanasiu, Virginia
%T The problem of determining estimators for different structural parameters in the case of credibility results for weighted contracts
%J Mathematica Bohemica
%D 2007
%P 389-405
%V 132
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.133964/
%R 10.21136/MB.2007.133964
%G en
%F 10_21136_MB_2007_133964

[1] Bühlmann, H.: Optimale Prämienstufensysteme. Mitt. Verein. Schweiz. Versicherungsmath. 64 (1964), 193–214.

[2] Bühlmann, H.: Mathematical Methods in Risk Theory. Springer, Berlin, 1970. | MR

[3] Daykin, C. D., Pentikäinen, T., Pesonen, M.: Practical Risk Theory for Actuaries. Chapman & Hall, 1993. | MR

[4] De Vylder, F.: Parameter estimation incredibility theory. ASTIN Bulletin 10 (1978), 99–112. | DOI | MR

[5] Goovaerts, M. J., Kaas, R., Van Heerwaarden, A. E., Bauwelinckx, T.: Effective Actuarial Methods, volume 3. Elsevier Science Publishers (1990), 105–239.

[6] Norberg, R.: On optimal parameter estimation in credibility. Insur. Math. Econ. 1 (1982), 73–80. | DOI | MR | Zbl

[7] Sundt, B.: On choice of statistics in credibility estimation. Scand. Actuar. J. (1979), 115–123. | DOI | MR | Zbl

[8] Sundt, B.: An Introduction to Non-Life Insurance Mathematics. Verlag Versicherungswissenschaft, Karlsruhe, 1984, pp. 22–54. | MR | Zbl

Cité par Sources :