Perhitungan premi asuransi kendaraan bermotor berdasarkan jenis jaminan dengan model multivariate Poisson regression = Premium pricing for vehicle insurance based on type of coverage using multivariate Poisson regression model

Dominique, Nancy Nikentary (2024) Perhitungan premi asuransi kendaraan bermotor berdasarkan jenis jaminan dengan model multivariate Poisson regression = Premium pricing for vehicle insurance based on type of coverage using multivariate Poisson regression model. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Sebagian besar perusahaan telah mempertimbangkan pemodelan premi berdasarkan jenis jaminan. Penelitian ini telah membangun premi dengan mempertimbangkan enam jenis jaminan yang ada, yaitu damage, fire, other, theft, Third Party Liability (TPL), dan windscreen. Selain itu, penelitian ini juga mempertimbangkan ketergantungan pada beberapa jenis jaminan jumlah klaim. Penelitian ini telah membangun empat model multivariate Poisson regression, yaitu model jumlah klaim dengan dua jenis jaminan (TPL dan windscreen) dengan satu variabel penjelas, lima variabel penjelas, model jumlah klaim tiga jenis jaminan (theft, TPL, dan windscreen) dengan satu variabel penjelas, dan enam variabel penjelas. Selain itu, penelitian ini juga membangun Generalized Linear Model (GLM) besar klaim untuk masing-masing jenis jaminan dengan pendekatan MLE menggunakan distribusi Gamma, distribusi Normal, dan distribusi Inverse Gaussian. Model premi murni dibangun dengan mengasumsikan jumlah klaim dan besar klaim saling bebas, sehingga premi murni diperoleh dengan perkalian hasil prediksi jumlah klaim dengan hasil prediksi besar klaim. Berdasarkan analisis menggunakan RMSE, diperoleh bahwa model Poisson Bayesian-Inverse Gaussian MLE dua jenis jaminan dengan satu variabel dan model Poisson MLE-Normal MLE tiga jenis jaminan adalah model terbaik untuk memprediksi premi murni dengan dua jenis jaminan dan tiga jenis jaminan secara bersamaan. Berdasarkan analisis menggunakan rataan premi murni, diperoleh bahwa model Poisson Bayesian-Gamma MLE dua jenis jaminan dengan satu variabel dan model Poisson Bayesian-Gamma MLE tiga jenis jaminan dengan satu variabel adalah model terbaik untuk memprediksi premi murni dengan dua jenis jaminan dan tiga jenis jaminan secara bersamaan. / Most insurance companies have considered premium modeling based on insurance types. This research has developed premiums by considering six existing insurance types: damage, fire, other, theft, Third Party Liability (TPL), and windscreen. Additionally, this study also considers the dependency on the number of claims for several types of insurance. Four multivariate Poisson regression models have been constructed, including a model for the number of claims with two types of insurance (TPL and windscreen) with one explanatory variable, a model for the number of claims with two types of insurance (TPL and windscreen) with five explanatory variables, a model for the number of claims with three types of insurance (theft, TPL, and windscreen) with one explanatory variable, and a model for the number of claims with three types of insurance (theft, TPL, and windscreen) with six explanatory variables. Furthermore, this study has also modeling Generalized Linear Models (GLMs) for severity of claims for each type of insurance using the Maximum Likelihood Estimation (MLE) approach with Gamma, Normal, and Inverse Gaussian distributions. Pure premium models are constructed by assuming that the number of claims and the severity of claims are independent. Thus, pure premiums are obtained by multiplying the predicted number of claims by the predicted severity of claims. Based on the analysis using Root Mean Square Error (RMSE), it is found that the Poisson Bayesian-Inverse Gaussian MLE model for two types of insurance with one variable and the Poisson MLE-Normal MLE model for three types of insurance are the best models for predicting pure premiums with two types of insurance and three types of insurance simultaneously. Based on the analysis using the average pure premium, it is found that the Poisson Bayesian-Gamma MLE model for two types of insurance with one variable and the Poisson Bayesian-Gamma MLE model for three types of insurance with one variable are the best models for predicting pure premiums with two types of insurance and three types of insurance simultaneously.

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