Penerapan Metode Limited-Fluctuation Credibility dalam Menentukan Premi Murni pada Asuransi Kendaraan Bermotor di PT XYZ

<p><strong>Abstract. </strong>This paper discusses the method of limited-fluctuation credibility, also known as classic credibility. Credibility theory is a technique for predicting future premium rates based on past experience data. Limited fluctuation credibility consists of two credibility, namely full credibility if Z = 1 and partial credibility if Z &lt;1. Full credibility is achieved if the amount of recent data is sufficient for prediction, whereas if the latest data is insufficient then the partial credibility approach is used. Calculations for full and partial credibility standards are used for loss measures such as frequency of claims, size of claims, aggregate losses and net premiums. The data used in this paper is secondary data recorded by the company PT. XYZ in 2014. This data contains data on the frequency of claims and the size of the policyholder's partial loss claims for motor vehicle insurance products category 4 areas 1. Based on the results of the application, the prediction of pure premiums for 2015 cannot be fully based on insurance data for 2014 because the credibility factor value is less than 1. So based on the limited-fluctuation credibility method, the prediction of pure premiums for 2015 must be based on manual values for pure premiums as well as insurance data for 2014. If manual values for pure premium is 2,000,000 rupiah, then the prediction of pure premium for 2015 is 1,849,342 rupiah.</p><p><strong>Keywords</strong><strong>: </strong>limited fluctuation credibility, full credibility, partial credibility and partial loss</p>

Weather index insurance will offset heat-induced rice loss under global warming

Global warming threatens food security through causing increasing and severe yield losses from heat extremes, especially for smallholder rice-cropping farmers in Asia. Weather index insurance (WII) could transfer weather-related risks, secure farms’ income, and recover agricultural systems. Under future warming scenarios, however, the related studies are still scarce. Here, compared with the historical period (1961-2010), heat-induced loss will approximately increase by up to 5%, 18%, and 26% at 2100 under three shared socioeconomic pathways of CMIP6, respectively. As an ex-ante strategy, county-specific WII will improve farmers’ income by up to 13% and stabilize it by up to 36%, even though the pure premium rate of WII will increase by 10% at 2050 and by 30% at 2100. For the first time, our study proves WII is one effective adaptation strategy for the most susceptible farmers under global warming and has the potential to be applied for other crops and countries.

Determination of Critical Productivity Level on Cluster-Based Area of Rice Crop Insurance in Java

<strong>Indonesian</strong><br />Kesenjangan tingkat produktivitas padi di Indonesia cukup besar yang di antaranya dipengaruhi oleh luasnya wilayah pertanaman. Hal ini berdampak pada desain dan penerapan model Asuransi Usaha Tani Padi (AUTP) berbasis produktivitas. Perluasan klaster pada tingkat provinsi diperkirakan dapat mengurangi keragaman produktivitas di tingkat wilayah kota/kabupaten sebagai risiko dasar pemanfaatan skema AUTP berbasis klaster. Klaster, sebagai wilayah atau zona, diperlukan untuk menentukan indeks kritis produktivitas yang akurat dalam rangka penghitungan tingkat premi yang tepat. Kajian ini bertujuan untuk menentukan tingkat produktivitas kritis pada lahan padi yang menerapkan skema AUTP. Kajian ini menggunakan analisis statistik dengan pendekatan batas bawah <em>Two Sigma</em> yang dapat dianggap sebagai batas produktivitas kritis untuk setiap klaster. Teknik ini memberikan persentase yang rendah atas klaim yang terjadi, serta ekspektasi dan simpangan baku dari risiko dasar kerugian. Tarif premi murni yang diperoleh adalah Rp85.191,18, hampir 2,5 kali lipat lebih kecil dibandingkan dengan menggunakan teknik lain sebagai batas poduktivitas. Hasil kajian ini mengungkapkan bahwa penggunaan skema berbasis klaster lebih baik dari skema berbasis provinsi, sebagaimana ditunjukkan oleh nilai TVaR. Kajian ini menyarankan agar Kementerian Pertanian dapat merancang model AUTP berbasis produktivitas berdasarkan klaster dengan setiap klaster memiliki nilai indeks produktivitas kritis yang berbeda untuk menetapkan tingkat premi yang dikenakan.<br /><br /><br /><strong>English</strong><br />There is a large gap in productivity of paddy in Indonesia which is, among others affected by the area size of crop planting. This condition should influence the design and application model of the rice crop insurance scheme. Developing clusters under the province level is recommended to reduce the heterogeneous productivity as basis risk within regencies/municipalities in improving the area yield index of crop insurance policy in Indonesia. Clusters, as the zone, are necessary to determine accurate critical yield index leading to a more precise premium rate making. This study aims to determine critical productivity level on rice crop insurance area. This study applied statistical analysis using the lower bound of Two Sigma as a critical yield for each cluster. This technique provides a small percentage of claim, and the expectation and standard deviation of basis risk loss. The pure premium rate obtained from the analysis is IDR85,191.18, that is almost 2.5 times less than using other methods as trigger productivity. The analysis result emphasized that the use of the cluster-based scheme is better than the province-based as shown by TVaR value. The study suggests that the Ministry of Agriculture could design the area yield index based on clusters as each cluster will have a different critical productivity index with adjusted premium rate value.

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

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.

Determining Critical Yield Index of Area Yield Insurance based on Basis Risk Constraint

Area yield index insurance at district level faces heterogeneous basis risk due to geographical conditions which implies to obtain unprecise critical index . Clustering and zone-based area yield scheme can reduce heterogeneous basis risk that leads to determine the suitable alternative for . On the previous research, we have obtained 7 clusters and 2 level of paddy productivity based on clustering assumption from primary data in Java. The suitable clustering assumption for calculating is cluster based assumption, which gives the homogeneous paddy productivity under 7 clusters in Java. Therefore, our goal is to develop area yield index at district level (cluster based) with minimize basis risk at certain constraints for paddy farmer productivity in Java Indonesia. There are some methods for calculating such as mean, median, winsor mean, one sigma, two sigma and (first quartile) method on the basis risk constraints using confusion matrix. Furthermore, two basis risk constraints are the difference between overpayment and shortfall is not extremely far, and total basis risk does not exceed 20% of its total claim occurrence. Two sigma method has the lowest basis risk, overpayment, and shortfall, but it has lowest pure premium, small probability of claim, and low range of claim. Hence, we consider to use (first quartile) method as alternative and suitable method to calculate that satisfied two basis risk constraints. In conclusion, our research provides analytical calculation for area yield index at district level with pure premium as Rp 152,151 using ( method), which is sufficient to cover the total claim and consistent with the simulation.

Expected Value Premium Principle Pada Data Reasuransi

The amount of stop loss cover reinsurance using krone as Danish currency. The stop loss cover reinsurance scheme with a retention value of r = 50 million krone from fire insurance data in Denmark from 1980-1990 with truncate date at 10 million krone, resulting in a conditional expected value that decreases in value when the higher the threshold value. This is indicated by the threshold value of 1 = 2.976 resulting in pure premium of 1 = 0.1217, a threshold value of 2 = 10.0539 resulting in pure premium 2 = 0.0867 and a threshold value of 3 = 26.199 resulting in pure premium 3 = 0.0849. The use of expected value premium principle with the loading factor () is weighted to the value of the pure premium represented by. This is indicated by the weight of premium 1 = 0.13387, the weight of the premium 2 = 0.09537 and the weight of premium 3 = 0.09339.