Perhitungan premi dan cadangan premi untuk disability income insurance dengan thiele's differential equation dan pendekatan simulasi = Premium and premium reserve calculation for disability income insurance with thiele's differential equation and simulation approach

Rizal, Livia (2023) Perhitungan premi dan cadangan premi untuk disability income insurance dengan thiele's differential equation dan pendekatan simulasi = Premium and premium reserve calculation for disability income insurance with thiele's differential equation and simulation approach. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Disability income insurance merupakan program yang membayarkan sejumlah uang kepada tertanggung pada periode disabilitas sehingga berguna untuk melindungi pekerja dari risiko hilangnya pendapatan akibat cacat yang menghalanginya untuk bekerja. Digunakan data pekerja pria kelahiran 2001 yang tertanggung dalam asuransi sejak usia 20 hingga 66 tahun dari Social Security Administration. Berdasarkan data, dimodelkan suatu bentuk multiple state dengan mengasumsikan proses Markov yang memiliki 4 keadaan, yaitu aktif, cacat, pulih, dan meninggal. Data diolah untuk mendapatkan laju transisi dengan menggunakan teknik estimasi parameter. Menggunakan laju transisi tersebut, selanjutnya dihitung premi dan cadangan premi asuransi. Metode Thiele’s differential equation berhasil digunakan untuk menghitung premi dan cadangan premi kontinu. Didapatkan cadangan premi kontinu pada keadaan aktif, cacat, maupun pulih yang terus menurun seiring bertambahnya waktu, kecuali cadangan premi keadaan aktif yang akan naik kembali ketika mendekati akhir dari masa asuransi. Metode simulasi Monte Carlo digunakan untuk menghitung premi dan cadangan premi diskrit dari rata-rata nilai harapan di suatu waktu untuk sejumlah individu saling bebas. Dengan simulasi, produk asuransi dapat ditambahkan fitur seperti elimination period dan maximum benefit period sehingga didapatkan premi kontinu berkurang secara signifikan. Didapatkan pula cadangan premi diskrit di keadaan cacat dan pulih untuk asuransi yang menerapkan kedua fitur tersebut lebih rendah dibanding asuransi biasa, sedangkan cadangan pada keadaan aktif untuk asuransi biasa akan lebih rendah dibanding asuransi yang menerapkan elimination period dan maximum benefit period. Perhitungan menggunakan simulasi Monte Carlo membutuhkan banyak sampel sehingga diperlukan computational effort yang besar untuk mencapai hasil yang akurat. / Disability income insurance is a program which pays benefit for the insureds during periods of disability to protect them from risks of losing income when they are disabled. The data used are disability and death probability for insured male workers born in 2001 with an age range of 20 to 66 years old from Social Security Administration. Assuming Markov process, data are modeled into 4 states: active, disabled, recovered, and dead. Data are processed to calculate force of transitions using parameter estimation technique. After obtaining force of transitions, premium and premium reserve can be calculated. Thiele’s differential equation can be used to calculate continuous premium and premium reserve. Continuous premium reserve in active, disabled, and recovered states tend to decrease, except for reserve in active state during last year of insurance. In addition, Monte Carlo simulation method can be used to obtain discrete premium and premium reserve by calculating the average expected value from a number of independent individuals. With simulation, some features can be added to the product, such as elimination period and maximum benefit period so that premium will be more affordable. Discrete premium reserve in disabled and recovered states for insurance that applies those features is lower than ordinary insurance, meanwhile reserve in active state for ordinary insurance is lower than insurance that has elimination and maximum benefit period in it. Calculation using Monte Carlo simulation requires considerable amount of samples and great computational effort to achieve accurate results.

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