Perhitungan premi kredibilitas asuransi disabilitas di Amerika Serikat dengan model Buhlmann nonparametrik dan semiparametrik menggunakan aproksimasi kuadratik = Credibility premium estimastion of disability insurance in the United States with nonparametric and semiparametric Buhlmann model using q-credibility method

Lummawie, Clairine Betsy (2023) Perhitungan premi kredibilitas asuransi disabilitas di Amerika Serikat dengan model Buhlmann nonparametrik dan semiparametrik menggunakan aproksimasi kuadratik = Credibility premium estimastion of disability insurance in the United States with nonparametric and semiparametric Buhlmann model using q-credibility method. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Klasifikasi tingkat risiko tidak dapat dilakukan secara sempurna karena adanya faktor random chance pada kerugian asuransi. Oleh karena itu, pentingnya teori kredibilitas dalam penghitungan premi asuransi. Pada penelitian, dilakukan estimasi premi kredibilitas klaim asuransi disabilitas di Amerika Serikat serta analisis hasil dari estimasi. Estimasi dilakukan ke dalam dua skenario besar, skenario tanpa data tersensor dan skenario data tersensor, dengan tujuan untuk mendapatkan estimasi yang lebih akurat dan menguji konsistensi dari hasil analisis. Metode yang digunakan adalah metode premi kredibilitas empirikal standar dan pendekatan baru yang dikenal sebagai aproksimasi kuadratik atau q-credibility. Estimasi dilakukan pada model Buhlmann nonparametrik dan semiparametrik asumsi model distribusi normal menggunakan kedua metode, serta model Buhlmann-Straub nonparametrik menggunakan metode standar. Penelitian menunjukkan bahwa metode baru aproksimasi kuadratik memberikan estimasi yang sama baiknya dengan metode standar. Berdasarkan analisis Mean Squared Error, nilai MSE dengan metode aproksimasi kuadratik selalu lebih rendah daripada nilai MSE dengan metode standar karena adanya penambahan faktor kuadratik pada perhitungan premi sehingga memperkecil selisih jarak kuadrat antara estimasi dengan data aktual. Meskipun demikian, tidak berarti bahwa metode aproksimasi kuadratik selalu memberikan hasil estimasi yang lebih baik daripada metode standar. Berdasarkan analisis Mean Absolute Percentage Error, nilai MAPE estimasi dengan metode standar dapat lebih tinggi daripada nilai MAPE estimasi dengan metode aproksimasi kuadratik. Perbedaan hasil analisis MSE dan MAPE disebabkan oleh MSE kurang sesuai untuk menganalisis prediksi deret waktu dan MSE bergantung pada skala nilai, dimana variansi hasil estimasi di Amerika Serikat sangat luas. Meskipun demikian, berdasarkan analisis uji-t, kedua metode memberikan estimasi dengan tingkat akurasi yang sama baik. / Risk classification cannot be achieved with absolute precision due to the inherent presence of random chance in insurance losses. Therefore, the incorporation of credibility theory becomes imperative in the realm of insurance premium calculations. This study undertakes the estimation alongside a comprehensive analysis of disability insurance claim premiums in the United States. The estimations are conducted under two primary scenarios: uncensored data and censored data. The objectives are to attain more accurate estimations and to examine the consistency of the analytical outcomes. The methods used are the classic empirical credibility premium method and a new approach known q-credibility. These techniques are applied to both the nonparametric and semiparametric Buhlmann models assuming a normal distribution, as well as the nonparametric Buhlmann-Straub model using the classic method. The research shows that the q-credibility method yields estimations that are on par with the classic approach. Through an analysis of Mean Squared Error, it is observed that the MSE values associated with the q-credibility method consistently outperform those derived from the classic method due to the addition of quadratic factors in the premium calculation, which reduces the squared distance between the estimation and the actual data. However, it is essential to emphasize that the q-credibility method does not invariably yield superior estimations compared to the classic method. Based on the Mean Absolute Percentage Error analysis, the MAPE values obtained through the classic method may surpass those derived from the q-credibility method. The dissimilarity between the results of the MSE and MAPE analyses arises due to the inadequacy of MSE in evaluating time series predictions, as well as its dependence on the scale of values, whereas the estimation variances in the United States are quite wide. Nevertheless, based on the results of t-test, both methods offer estimations with comparable levels of accuracy.

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