Calculation and Management of Premium Funds in Sharia Insurance (Ta'min, Takaful or Tadhamun)

Khusnul Khotimah, Mahmudi Mahmudi, Nina Fitriyati

Abstract


Abstract

This research discusses the calculation of the premium of term life-insurance based on sharia principles. The difference between the conventional method and the sharia principle is in the concept of interest rates. In this research, the concept of interest in the conventional method is replaced by the Return on Investment (ROI) that changes stochastically following the Langevin type model. The Monte-Carlo simulation is applied to generate the ROI with some initial values. On the mechanism of premium management, we apply the system without a saving element and the Al-Mudharabah relationship where the participants will get a sharing-profit of the operating surplus if they don’t make a claim until the end of the agreement period. We assume that the administrative expenses only charged in the first year. Therefore, the operating surplus will be greater after the first year. In addition, we do 20 times of Monte–Carlo simulations to generate the ROI with initial value are 7.5%, 9%, and 10%. The result shows that the annual premiums become smaller when the ROI become greater and vice versa. This is because the company get a smaller return when the initial of ROI is small. So the annual premium will be greater. The annual premium for male participants is greater than women because the rate of death of men is greater than women. The other factors that make the annual premium more expensive are length of the agreement and greater compensation.

Keywords: Langevin type model, stochastic differential equation, system without a saving element, Al-Mudharabah principle, Monte–Carlo simulation.

 

Abstrak

Penelitian ini membahas mengenai perhitungan dana premi asuransi jiwa berjangka berdasarkan prinsip–prinsip syariah. Perbedaan antara metode konvensional dengan prinsip syariah adalah pada konsep tingkat bunga. Pada penelitian ini, konsep bunga digantikan dengan nilai Return on Investment (ROI) yang berubah secara stokastik mengikuti model tipe Langevin. Simulasi Monte–Carlo diterapkan untuk membangkitkan nilai ROI menggunakan beberapa nilai awal. Pada mekanisme pengelolaan dana premi, kami menerapkan sistem tanpa unsur tabungan dan hubungan Al-Mudharabah dimana peserta akan mendapatkan bagi hasil atas surplus operasional jika peserta tersebut tidak melakukan klaim sampai akhir masa perjanjian. Kami mengasumsikan bahwa biaya administrasi hanya dibebankan pada tahun pertama. Sehingga surplus operasional akan menjadi lebih besar setelah tahun pertama. Selain itu, kami melakukan 20 kali simulasi Monte–Carlo untuk membangkitkan ROI dengan nilai awal 7.5%, 9%, dan 10%. Hasil menunjukkan bahwa premi tahunan akan semakin kecil jika nilai awal dari ROI membesar dan sebaliknya. Hal ini disebabkan oleh keuntungan perusahaan yang kecil jika nilai awal ROI semakin kecil sehingga premi tahunan haruslah lebih besar. Premi tahunan untuk peserta laki-laki cenderung lebih besar daripada premi tahunan peserta wanita. Hal ini karena tingkat kematian laki-laki lebih tinggi daripada wanita. Faktor lain yang membuat premi tahunan lebih besar adalah lamanya masa kontrak asuransi dan kompensasi yang semakin besar.

Kata kunci: Model tipe Langevin, persamaan diferensial stokastik, sistem tanpa unsur tabungan, prinsip Al-Mudharabah, simulasi Monte–Carlo.


References


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Full Text: PDF

DOI: 10.15408/inprime.v1i2.13631

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