Dynamic credibility with outliers and missing observations

Tomáš Cipra

Applications of Mathematics (1996)

  • Volume: 41, Issue: 2, page 149-159
  • ISSN: 0862-7940

Abstract

top
In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the M -estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.

How to cite

top

Cipra, Tomáš. "Dynamic credibility with outliers and missing observations." Applications of Mathematics 41.2 (1996): 149-159. <http://eudml.org/doc/32942>.

@article{Cipra1996,
abstract = {In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.},
author = {Cipra, Tomáš},
journal = {Applications of Mathematics},
keywords = {credibility; actuarial science; outliers; missing observations; robust Kalman filter; shrinkage; time series; risk; robust Kalman filter; time series; risk; -estimation; credibility models; outliers; missing observations; shrinkage},
language = {eng},
number = {2},
pages = {149-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dynamic credibility with outliers and missing observations},
url = {http://eudml.org/doc/32942},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Cipra, Tomáš
TI - Dynamic credibility with outliers and missing observations
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 2
SP - 149
EP - 159
AB - In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the $M$-estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.
LA - eng
KW - credibility; actuarial science; outliers; missing observations; robust Kalman filter; shrinkage; time series; risk; robust Kalman filter; time series; risk; -estimation; credibility models; outliers; missing observations; shrinkage
UR - http://eudml.org/doc/32942
ER -

References

top
  1. Alternative Methods of Regression, Wiley, New York, 1993. (1993) MR1227984
  2. Excess claims and data trimming in the context of credibility rating procedures, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 82 (1982), 117–147. (1982) 
  3. Glaubwürdigkeit für Schadensätze, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 70 (1970), 11–113. (1970) 
  4. Robust Kalman filter and its application in time series analysis, Kybernetika 27 (1991), 481–494. (1991) MR1150938
  5. Credibility theory and the Kalman filter, Insurance: Mathematics and Economics 2 (1983), 281–286. (1983) MR0721576
  6. 10.1017/S0515036100007054, ASTIN Bulletin 12 (1981), 115–131. (1981) MR0660732DOI10.1017/S0515036100007054
  7. Practical models in credibility theory, including parameter estimation, Premium Calculation in Insurance, F. deVylder, M. Goovaerts, J Haezendonck (eds.), Reidel, 1984. (1984) MR0786667
  8. Robust regression: Different approaches to numerical solution and algorithms, Research Report No. 6 (1975), ETH Zürich. 
  9. Credibility formulas of the updating type, Transactions of the Society of Actuaries 27 (1975), 31–46. (1975) MR0411094
  10. 10.2143/AST.23.1.2005104, ASTIN Bulletin 23 (1993), 117–143. (1993) DOI10.2143/AST.23.1.2005104
  11. Credibility for regression models with applications to trend, Credibility: Theory and Applications, P.M. Kahn (ed.), Academic Press, New York, 1975. (1975) MR0411061
  12. 10.1017/S0020268100036672, Journal of Institute of Actuaries 116 (1989), 513–528. (1989) DOI10.1017/S0020268100036672
  13. Robust Statistics, Wiley, New York, 1981. (1981) Zbl0536.62025MR0606374
  14. 10.1080/03461238.1982.10405260, Scandinavian Actuarial Journal (1982), 129–142. (1982) Zbl0503.62088MR0685879DOI10.1080/03461238.1982.10405260
  15. Large claims in credibility, Blätter der Deutschen Gesellschaft für Versicherungsmathematik 20 (1991), 123–150. (1991) Zbl0738.62097
  16. Empirical Kalman-credibility, Blätter der Deutschen Gesellschaft für Versicherungsmathematik 22 (1995), 17–28. (1995) Zbl0817.62086
  17. 10.2143/AST.24.2.2005066, ASTIN Bulletin 24 (1994), 221–233. (1994) DOI10.2143/AST.24.2.2005066
  18. 10.2143/AST.22.1.2005125, ASTIN Bulletin 22 (1992), 33–49. (1992) DOI10.2143/AST.22.1.2005125
  19. 10.2143/AST.21.1.2005402, ASTIN Bulletin 21 (1991), 73–91. (1991) DOI10.2143/AST.21.1.2005402
  20. 10.1002/for.3980120102, Journal of Forecasting 12 (1993), 1–11. (1993) DOI10.1002/for.3980120102
  21. 10.1080/03461238.1987.10413824, Scandinavian Actuarial Journal (1987), 128–156. (1987) Zbl0656.62108MR0943577DOI10.1080/03461238.1987.10413824
  22. 10.1080/03610928908829936, Commun. Statist. – Theory Meth. 18 (1989), 817–833. (1989) MR1001623DOI10.1080/03610928908829936
  23. 10.1080/03610919508813252, Commun. Statist. – Simulation and Computation 24 (1995), 461–488. (1995) MR1333047DOI10.1080/03610919508813252
  24. Stochastische Modellierung in der Erfahrungstarifierung, Blätter der Deutschen Gesellschaft für Versicherungsmathematik 20 (1992), 441–455. (1992) Zbl0781.62166
  25. 10.1080/03461238.1981.10413728, Scandinavian Actuarial Journal (1981), 3–21. (1981) Zbl0463.62093MR0611125DOI10.1080/03461238.1981.10413728

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.