MODEL STOKASTIK DENGAN PENDEKATAN GENERALIZED LINEAR MODEL UNTUK MENGESTIMASI CADANGAN KLAIM INCURRED BUT NOT REPORTED
Abstract
One of the crucial things in the insurance business is determining the amount of IBNR claim reserves. The amount of IBNR's claim reserves is uncertain so it is necessary to estimate as accurately as possible. The estimation results of IBNR's claim reserves will affect the solvency and sustainability of the company. To calculate the estimated IBNR claim reserves, several approaches are used both deterministically and stochastically. This study uses a stochastic model with the GLM approach for data that is assumed to have an ODP distribution. Besides, this study also uses 2 different methods to calculate parameter estimates in the model, namely by performing parameter transformations and using the Verbeek algorithm. This study will compare the results of the IBNR claim reserve estimation obtained using these two methods in estimating the parameters in the model. The estimation results obtained indicate that the value of the IBNR claim reserves is the same. The advantage of the Verbeek algorithm is that the resulting parameter values have interpretations.
Downloads
References
M. Rahmawati, I. Darti, dan M. Marjono, “Pencadangan Klaim IBNR dengan Pendekatan Distribusi Keluarga Tweedie pada Generalized Linear Model,” Limits J. Math. Its Appl., vol. 16, no. 1, hal. 11, Agu 2019, doi: 10.12962/limits.v16i1.5075.
T. Mack, “Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates,” ASTIN Bull., vol. 23, no. 2, hal. 213–225, Nov 1993, doi: 10.2143/ast.23.2.2005092.
L. Tee, M. Käärik, dan R. Viin, “On Comparison of Stochastic Reserving Methods with Bootstrapping,” Risks, vol. 5, no. 1, hal. 2, Jan 2017, doi: 10.3390/risks5010002.
S. Tuysuz dan P. Pekel, “A Comparison of Stochastic Claims Reserving Methods,” Eur. J. Bus. Manag. Res., vol. 4, no. 4, hal. 1–13, 2019, doi: 10.24018/ejbmr.2019.4.4.43.
E. Kremer, “IBNR-claims and the two-way model of anova,” Scand. Actuar. J., vol. 1982, no. 1, hal. 47–55, 1982, doi: 10.1080/03461238.1982.10405432.
A. E. Renshaw dan R. J. Verrall, “A Stochastic Model Underlying the Chain-Ladder Technique,” Br. Actuar. J., vol. 4, no. 4, hal. 903–923, Okt 1998, doi: 10.1017/s1357321700000222.
T. Mack dan G. Venter, “A comparison of stochastic models that reproduce chain ladder reserve estimates,” Insur. Math. Econ., vol. 26, no. 1, hal. 101–107, Feb 2000, doi: 10.1016/S0167-6687(99)00039-6.
P. D. England dan R. J. Verrall, “Stochastic Claims Reserving in General Insurance,” Br. Actuar. J., vol. 8, no. 3, hal. 443–518, Agu 2002, doi: 10.1017/s1357321700003809.
G. Taylor dan G. McGuire, Stochastic Loss Reserving Using Generalized Linear Models, no. 3. CAS MONOGRAPH SERIES, 2016.
R. Kaas, M. Goovaerts, J. Dhaene, dan M. Denuit, Modern Actuarial Risk Theory: Using R, Second. London: New York: Springer, 2008.
P. De Jong dan G. Z. Heller, Generalized linear models for insurance data. Cambridge University Press, 2008.
Y. Wilandari, S. H. Kartiko, dan A. R. Effendie, “Estimasi Cadangan Klaim Menggunakan Generalized Linear Model (GLM) dan Copula,” J. Gaussian, vol. 9, no. 4, hal. 411–420, 2020.
M. V. Wüthrich dan M. Merz, Stochastic Claims Reserving Methods in Insurance, 1 ed. Chichester: Wiley, 2008.
S. Triana, M. Novita, dan S. F. Sari, “The Benktander claim reserving method, combining chain ladder method and Bornhuetter-Ferguson method using optimal credibility,” in Journal of Physics: Conference Series, Jan 2021, vol. 1725, no. 1, doi: 10.1088/1742-6596/1725/1/012087.
A. Carrato, F. Concina, M. Gesmann, D. Murphy, M. Wüthrich, dan W. Zhang, “Claims reserving with R: ChainLadder-0.2.11 Package Vignette,” hal. 1–60, 2020.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
