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

2021 ◽  
Vol 3 (2) ◽  
pp. 115-127
Author(s):  
Tri Andika Julia Putra ◽  
Donny Citra Lesmana ◽  
I Gusti Putu Purnaba

ABSTRAKSeorang 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. ABSTRACTIt 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.

2002 ◽  
Vol 32 (1) ◽  
pp. 143-157 ◽  
Author(s):  
Gordon K. Smyth ◽  
Bent Jørgensen

AbstractWe reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.


2007 ◽  
Vol 37 (2) ◽  
pp. 345-364 ◽  
Author(s):  
Gary G. Venter

The formulation of generalized linear models in Klugman, Panjer and Willmot (2004) is a bit more general than is often seen, in that the residuals are not restricted to following a member of the exponential family. Some of the distributions this allows have potentially useful applications. The cost is that there is no longer a single form for the likelihood function, so each has to be fit directly. Here the use of loss distributions (frequency, severity and aggregate) in generalized linear models is addressed, along with a few other possibilities.


2007 ◽  
Vol 37 (02) ◽  
pp. 345-364 ◽  
Author(s):  
Gary G. Venter

The formulation of generalized linear models in Klugman, Panjer and Willmot (2004) is a bit more general than is often seen, in that the residuals are not restricted to following a member of the exponential family. Some of the distributions this allows have potentially useful applications. The cost is that there is no longer a single form for the likelihood function, so each has to be fit directly. Here the use of loss distributions (frequency, severity and aggregate) in generalized linear models is addressed, along with a few other possibilities.


Risks ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 79 ◽  
Author(s):  
Pigeon ◽  
Duval

In this paper, we propose models for non-life loss reserving combining traditionalapproaches such as Mack’s or generalized linear models and gradient boosting algorithm in anindividual framework. These claim-level models use information about each of the payments madefor each of the claims in the portfolio, as well as characteristics of the insured. We provide an examplebased on a detailed dataset from a property and casualty insurance company. We contrast sometraditional aggregate techniques, at the portfolio-level, with our individual-level approach and wediscuss some points related to practical applications.


2014 ◽  
Vol 1 (1) ◽  
pp. 371-401
Author(s):  
Y. Lu ◽  
S. Chatterjee

Abstract. Exponential family statistical distributions, including the well-known Normal, Binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that drive the data under. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular Normal distributional assumption dependent cumulative sum (Gaussian-CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, to understand whether the nature of these tropical storms has remained stable over the last few decades.


2014 ◽  
Vol 21 (6) ◽  
pp. 1133-1143
Author(s):  
Y. Lu ◽  
S. Chatterjee

Abstract. Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.


Sign in / Sign up

Export Citation Format

Share Document