Perhitungan Premi Asuransi Penyakit Kritis Berdasarkan Hukum Mortalitas Gompertz dan Weibull Menggunakan Suku Bunga Stokastik

Handayaningrum, Amelia Cahyani (2024) Perhitungan Premi Asuransi Penyakit Kritis Berdasarkan Hukum Mortalitas Gompertz dan Weibull Menggunakan Suku Bunga Stokastik. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Berdasarkan data dari Laporan Nasional Riskesdas (Riset Kesehatan Dasar) 2018 dan World Health Organization (WHO), penyakit kritis merupakan salah satu penyebab kematian tertinggi di Indonesia. Tingginya biaya perawatan untuk penyakit kritis menjadi salah satu permasalahan yang dihadapi penderita penyakit kritis. Salah satu pengembangan asuransi kesehatan yang terkenal adalah asuransi penyakit kritis yang memberikan pembayaran sekaligus (lump sum) kepada pemegang polis ketika terdiagnosis dengan penyakit kritis tertentu. Proses perubahan status kesehatan pemegang polis dapat digambarkan dengan model multiple state di mana komponen utama model multiple state ialah perhitungan intensitas transisi dan probabilitas transisi berdasarkan konsep rantai Markov. Untuk memperoleh perhitungan intensitas transisi dan probabilitas transisi yang akurat, diperlukan cakupan data yang luas dan komprehensif serta bersifat kontinu. Bagaimanapun juga, data seperti itu relatif sulit didapatkan atau bahkan tidak tersedia. Dalam penelitian ini, perhitungan premi asuransi penyakit kritis menggunakan data yang relatif mudah didapatkan, yaitu data jumlah kematian dan jumlah penderita penyakit kritis berdasarkan jenis kelamin dan kelompok usia. Selanjutnya, data diskrit tersebut dilakukan fitting dengan force of mortality hukum mortalitas Gompertz dan Weibull, lalu untuk memastikan bahwa data yang tersedia mengikuti hukum mortalitas Gompertz dan Weibull, maka dilakukan uji statistik Wald. Data dalam penelitian ini diperoleh dari RSUD Kabupaten Nganjuk tahun 2022, laman resmi BPS Nganjuk, dan laman resmi Bank Indonesia. Perhitungan premi asuransi penyakit kritis dihitung menggunakan portfolio percentile premium principle dan menggunakan suku bunga stokastik model Vasicek dan CIR. Hasil dalam penelitian ini diperoleh bahwa perhitungan premi menggunakan suku bunga stokastik model Vasicek dan CIR menghasilkan nilai yang hampir sama, tetapi benefit yang dihasilkan suku bunga stokastik model Vasicek lebih tinggi daripada CIR. Selain itu, besar premi untuk asuransi penyakit kritis tipe polis partial acceleration diperoleh hasil yang paling tinggi, lalu diikuti dengan tipe polis full acceleration, dan yang terakhir ialah stand alone. Berdasarkan hukum mortalitas, secara garis besar hukum mortalitas Weibull menghasilkan nilai premi yang lebih tinggi untuk tipe polis stand alone. Sedangkan hukum mortalitas Gompertz menghasilkan nilai premi yang lebih tinggi untuk tipe polis partial acceleration dan full acceleration.
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Based on data from the 2018 National Basic Health Research Report and the World Health Organization (WHO), critical illness is one of the leading causes of death in Indonesia. The high cost of treatment for critical illnesses is one of the problems faced by people with critical illnesses. One of the well-known developments in health insurance is critical illness insurance which provides a lump sum payment to the policy holder when diagnosed with a certain critical illness. The process of changing the policyholder's health status can be described using a multiple state model where the main component of the multiple state model is the calculation of transition intensity and transition probability based on the Markov chain concept. To obtain accurate calculations of transition intensity and transition probability, extensive, comprehensive and continuous data coverage is required. However, such data are relatively difficult to obtain or even unavailable. In this research, critical illness insurance premiums will be calculated using data that is relatively easy to obtain, that is data on the number of deaths and the number of critical illness sufferers based on gender and age group. Furthermore, this discrete data will be fitted using the Gompertz and Weibull mortality laws and to ensure that the available data follow Gompertz and Weibull's mortality laws, Wald's statistical tests will be conducted. The data in this research was obtained from the RSUD Nganjuk 2022, official website of BPS Nganjuk, and official website of BI. The calculation of critical illness insurance premiums is calculated using the portfolio percentile premium principle and Vasicek and CIR type stochastic interest rates. The results of this research show that premium calculations using the Vasicek and CIR model stochastic interest rates produce almost the same values, but the benefits generated by the Vasicek model stochastic interest rates are higher than CIR. The premium for critical illness insurance with the partial acceleration policy type obtained the highest results, followed by the full acceleration policy type, and the last one is stand alone. Based on the law of mortality, in general the Weibull mortality law produces a higher premium value for the stand-alone policy type. Meanwhile, Gompertz's mortality law produces higher premium values for partial acceleration and full acceleration policy types.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Asuransi Penyakit Kritis, Hukum Mortalitas Model Multiple State, Suku Bunga Stokastik, Critical Illness Insurance, Multiple State Model, Morbidity and Mortality, Mortality Law, Stochastic Interest Rate
Subjects:	Q Science > QA Mathematics > QA273.6 Weibull distribution. Logistic distribution. Q Science > QA Mathematics > QA274.2 Stochastic analysis Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis
Depositing User:	Amelia Cahyani Handayaningrum
Date Deposited:	22 Jul 2024 05:57
Last Modified:	22 Jul 2024 05:57
URI:	http://repository.its.ac.id/id/eprint/108632

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