Penghitungan Premi Asuransi Kendaraan Bermotor Menggunakan Generalized Linear Models dengan Distribusi Tweedie

Tri Andika Julia Putra, Donny Citra Lesmana, I Gusti Putu Purnaba

Abstract


ABSTRAK


Seorang aktuaris mempunyai tugas penting dalam menentukan harga premi yang sesuai untuk setiap nasabah dengan risiko dan karakteristik yang berbeda. Banyak variabel yang dapat mempengaruhi harga premi. Oleh karena itu, aktuaris harus mengetahui variabel-variabel yang berpengaruh signifikan terhadap premi. Tujuan dari penelitian ini adalah untuk menentukan variabel yang dapat mempengaruhi besaran premi murni menggunakan distribusi campuran dalam menentukan besarnya premi melalui Generalized Linear Models (GLM) serta menentukan model harga premi yang sesuai berdasarkan variabel-variabel yang mempengaruhinya. Salah satu analisis statistik yang dapat digunakan untuk memodelkan premi asuransi adalah Generalized Linear Models. GLM merupakan perluasan dari model regresi klasik yang dapat mengakomodasi fleksibilitas untuk menggunakan beberapa distribusi data tetapi terbatas pada distribusi keluarga eksponensial. Dalam model GLM, premi diperoleh dengan mengalikan nilai ekspektasi bersyarat dari frekuensi klaim dan biaya klaim. Berdasarkan penelitian yang telah dilakukan diketahui bahwa frekuensi klaim dan besarnya klaim mengikuti distribusi Tweedie. Dari kedua model tersebut diketahui bahwa variabel yang mempengaruhi premi murni adalah jumlah anak, pendapatan per bulan, status pernikahan, pendidikan, pekerjaan, penggunaan kendaraan, besarnya bluebook yang dibayarkan, dan jenis kendaraan nasabah. Hal ini menunjukkan bahwa model GLM merupakan model yang representatif dan berguna bagi perusahaan asuransi.

 

ABSTRACT

It is an important task for an actuary in determining the appropriate premium price for each customer with different risks and characteristics. Many variables can affect the premium price. Therefore, actuaries must determine the variables that significantly affect the premium. The purpose of this study is to determine the variables that can affect the amount of pure premium using a mixed distribution in determining the amount of premium through Generalized Linear Models (GLM) and determine the appropriate premium price model based on the variables that influence it. One of the statistical analyzes that can be used to model insurance premiums is the Generalized Linear Models. GLM is an extension of the classic regression model that can accommodate the flexibility of its users to use multiple data distributions but is limited to the exponential family distribution. In the GLM model, the premium is obtained by multiplying the conditional expected value of the frequency of claims and the cost of claims. Based on the research that has been done, it is known that the frequency of claims and the size of claims follow the Tweedie distribution. From the two models, it is known that the variables affecting the pure premium are the number of children, monthly income, marital status, education, occupation, vehicle use, the number of bluebooks paid, and the type of vehicle from the customer. This shows that the GLM model is a representative and useful model for the insurance company business.


Keywords


Premiums of Insurance; Generalized Linear Models; Frequency of Claims; Cost of Claim; Tweedie Distribution

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References


B. H. dan H. B. U. A. M. Agung-RI, [KUHD] Kitab Undang-undang Hukum Dagang Tahun 2009 Bab 9 Pasal 246 Tentang Asuransi atau Pertanggungan Seumurnya. Bhuana Ilmu Populer, 2017.

S. Asmussen and M. Steffensen, Probability Theory and Stochastic Modelling: Risk and insurance. Switzerland: Springer, 2020.

P. R. Kongstvedt, Health Insurance and Managed Care, 5 th. Burlington: Jones And Bartlett Learning, 2020.

P. Shi, X. Feng, and A. Ivantsova, “Dependent frequency-severity modeling of insurance claims,” Insur. Math. Econ., vol. 64, pp. 417–428, 2015, doi: 10.1016/j.insmatheco.2015.07.006.

E. Frees, G. Lee, and L. Yang, “Multivariate Frequency-Severity Regression Models in Insurance,” Risks, vol. 4, no. 1, p. 4, 2016, doi: 10.3390/risks4010004.

M. David, “Auto insurance premium calculation using generalized linear models,” Procedia Econ. Financ., vol. 20, no. 15, pp. 147–156, 2015, doi: 10.1016/S2212-5671(15)00059-3.

N. Iyit, H. Yonar, and A. Genc, “Generalized Linear Models for European Union Countries Energy Data,” Acta Phys. Pol. A, vol. 130, no. 1, 2016, doi: 10.12693/APhysPolA.130.397.

J. Garrido, C. Genest, and J. Schulz, “Generalized linear models for dependent frequency and severity of insurance claims,” Insur. Math. Econ., vol. 70, pp. 205–215, 2016, doi: 10.1016/j.insmatheco.2016.06.006.

H. Fitrianti, “Model Faktor-Faktor Banyaknya Kecelakaan Lalu Lintas Pada Kendaraan Sepeda Motor Dengan Pendekatan Generalized Linear Model,” Magistra, vol. 4, no. 2, pp. 94–104, 2017.

W. H. Bonat, B. Jorgensen, C. Kokonendji, and J. Hinde, “Extended Poisson – Tweedie : Properties and Regression Models for Count Data,” Stat. Modelling, pp. 1–26, 2017.

Sukono, Riaman, E. Lesmana, R. Wulandari, H. Napitupulu, and S. Supian, “Model estimation of claim risk and premium for motor vehicle insurance by using Bayesian method,” IOP Conf. Ser. Mater. Sci. Eng., vol. 300, no. 1, 2018, doi: 10.1088/1757-899X/300/1/012027.

B. Debrabant, U. Halekoh, W. H. Bonat, D. L. Hansen, J. Hjelmborg, and J. Lauritsen, “Identifying traffic accident black spots with Poisson-Tweedie models,” Accid. Anal. Prev., vol. 111, pp. 147–154, 2018, doi: 10.1016/j.aap.2017.11.021.

D. Saha, P. Alluri, E. Dumbaugh, and A. Gan, “Application of the Poisson-Tweedie distribution in analyzing crash frequency data,” Accid. Anal. Prev., vol. 137, no. January, p. 105456, 2020, doi: 10.1016/j.aap.2020.105456.

N. Li, X. Peng, E. Kawaguchi, M. A. Suchard, and G. Li, “A scalable surrogate L0 sparse regression method for generalized linear models with applications to large scale data,” J. Stat. Plan. Inference, vol. 213, pp. 262–281, 2020, doi: 10.1016/j.jspi.2020.12.001.

S. A. Klugman, H. H. Panjer, and G. E. Willmot, Loss Models From Data ro Decisions, 5 th., vol. 6, no. 1. Hoboken, New Jersey: John Wiley & Sons, Inc., 2019.

A. Agresti, Foundations Linear Generalized Linear Models. Cambridge: John Wiley & Sons, Inc., 2015.

G. Z. Jong, P D, Heller, Generalized Linear Models for Insurance Data. Cambridge: Cambridge University Press, 2008.

M. Tweedie, “An Index Which Distinguishes Between Some Important Exponential Families. The Statistics: Applications and New Directions,” 1984.

U. Simsekli, A. T. Cemgil, and B. Ermis, “Learning Mixed Divergences in Coupled Matrix and Tensor Factorization Models,” in The Acoustics, Speech and Signal Processing (ICASSP), 2015, pp. 2120–2124.

O. Oznur and N. Iyit, “Modelling the US Diabetes Mortality Rates via Generalized Linear Model with the Tweedie Distribution,” Int. J. Sci. Res., vol. 7, no. 2, pp. 1326–1334, 2018, doi: 10.21275/ART2018368.

A. A. Khalin and E. B. Postnikov, “A wavelet-based approach to revealing the Tweedie distribution type in sparse data,” Phys. A Stat. Mech. its Appl., vol. 553, p. 124653, 2020, doi: 10.1016/j.physa.2020.124653.

E. W. Frees, Regression Modeling with Actuarial and Finansial Applications. Cambridge: Cambridge University Press, 2010.

E. T. Lee and J. W. Wang, Statistical Methods for Survival Data Analysis, 4 rd. Hoboken, New Jersey: John Wiley & Sons, Inc., 2013.




DOI: https://doi.org/10.34312/jjom.v3i2.10136



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