scholarly journals Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling

2002 ◽  
Vol 32 (1) ◽  
pp. 143-157 ◽  
Author(s):  
Gordon K. Smyth ◽  
Bent Jørgensen
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Likelihood Function ◽  
Poisson Model ◽  
Insurance Claims ◽  
Poisson Arrival ◽  
Insurance Claims Data ◽  
The Cost ◽  
Insurance Data

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.

scholarly journals Generalized Linear Models beyond the Exponential Family with Loss Reserve Applications

2007 ◽  
Vol 37 (2) ◽  
pp. 345-364 ◽  
Author(s):  
Gary G. Venter
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Likelihood Function ◽  
Loss Reserve ◽  
Loss Distributions ◽  
Single Form ◽  
The Cost

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.

scholarly journals Generalized Linear Models beyond the Exponential Family with Loss Reserve Applications

2007 ◽  
Vol 37 (02) ◽  
pp. 345-364 ◽  
Author(s):  
Gary G. Venter
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Likelihood Function ◽  
Loss Reserve ◽  
Loss Distributions ◽  
Single Form ◽  
The Cost

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.

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
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Insurance Company ◽  
Number Of Children ◽  
Multiple Data ◽  
Pure Premium ◽  
Premium Price ◽  
Tweedie Distribution ◽  
The Cost

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.

scholarly journals Overdispersed-Poisson Model in Claims Reserving: Closed Tool for One-Year Volatility in GLM Framework

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 139
Author(s):  
Stefano Strascia ◽  
Agostino Tripodi
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Poisson Model ◽  
Point Of View ◽  
Approximation Techniques ◽  
The Monte Carlo Method ◽  
Calculation Point ◽  
One Year ◽  
The One ◽  
Bootstrap Methodology

The aim of this paper is to carry out a closed tool to estimate the one-year volatility of the claims reserve, calculated through the generalized linear models (GLM), notably the overdispersed- Poisson model. Up to now, this one-year volatility has been estimated through the well-known bootstrap methodology that demands the use of the Monte Carlo method with a re-reserving technique. Nonetheless, this method is time consuming under the calculation point of view; therefore, approximation techniques are often used in practice, such as an emergence pattern based on the link between the one-year volatility—resulting from the Merz–Wüthrich method—and the ultimate volatility—resulting from the Mack method.

scholarly journals Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

2009 ◽  
Vol 4 (1) ◽  
pp. 7-31 ◽  
Author(s):  
D. H. Alai ◽  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Mean Square Error ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Poisson Model ◽  
Development Pattern ◽  
Mean Square ◽  
Conditional Mean ◽  
Major Subject ◽  
Chain Ladder

ABSTRACTThe prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

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