Analisis premi dan cadangan premi untuk model multiple state diskrit dengan simulasi Monte Carlo = Premium and premium reserve analysis for discrete multiple state model with Monte Carlo simulation

Felia, Felia (2020) Analisis premi dan cadangan premi untuk model multiple state diskrit dengan simulasi Monte Carlo = Premium and premium reserve analysis for discrete multiple state model with Monte Carlo simulation. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Asuransi adalah perjanjian antara dua pihak, yaitu pihak tertanggung, yang berkewajiban membayar premi dan pihak penanggung yang berkewajiban memberi perlindungan dalam bentuk benefit. Kondisi pihak tertanggung dapat digambarkan dengan model multiple state. Terdapat lima jenis asuransi yang berbeda masa pembayaran benefit dan preminya, yaitu asuransi seumur hidup, berjangka, dwiguna, dwiguna murni, dan tangguhan. Sebelum perjanjian dibuat, pihak penanggung harus menghitung nilai premi yang sesuai dengan benefit yang ditawarkan. Setelah kontrak berjalan, pihak penanggung juga harus menghitung cadangan premi yang perlu disediakan jika total nilai premi lebih kecil dari total benefit yang akan diberikan. Simulasi Monte Carlo dapat digunakan untuk menghitung nilai premi dan cadangan premi dengan menghitung rata-rata dari hasil sejumlah kejadian acak yang saling bebas. Dalam perhitungan premi dan cadangan premi, terdapat variabel-variabel yang mempengaruhi perhitungan, seperti suku bunga dan deviasinya, masa kontrak, dan benefit. Suku bunga yang tinggi membuat nilai premi menurun dan cadangan premi semakin mendekati nol. Deviasi suku bunga yang besar membuat selisih nilai premi dengan dan tanpa deviasi cenderung semakin besar, begitu juga dengan cadangan premi. Benefit yang besar membuat nilai premi meningkat dan cadangan premi semakin menjauhi nol. Sementara itu, perubahan masa kontrak memberi pengaruh yang berbeda sesuai dengan jenis asuransinya. Masa kontrak yang lama membuat premi dan cadangan premi asuransi berjangka dan dwiguna cenderung meningkat, premi asuransi dwiguna murni menurun, sementara cadangan preminya berubah sesuai status tertanggung, serta premi dan cadangan premi tangguhan yang tidak mengikuti pola tertentu. Untuk asuransi seumur hidup, suku bunga memiliki pengaruh paling besar. Untuk asuransi dwiguna murni dan tangguhan, masa kontrak memiliki pengaruh paling besar. Sementara itu, untuk asuransi berjangka dan dwiguna, suku bunga dan masa kontrak memiliki pengaruh paling besar, sesuai dengan status tertanggung. / Insurance is a contract between two parties, namely an insured who’s obliged to pay premium and an insurer who’s obliged to give protection in the form of benefit. The insured’s condition can be illustrated in a multiple state model. There are five insurance types with different time for premium and benefit payments, namely: whole life insurance, term insurance, endowment insurance, pure endowment insurance, and deferred insurance. Before the contract is made, the insurer has to calculate the premium according to the benefit offered. After the contract is made, the insurer has to calculate the premium reserve needed if the total premium is less than the total benefit to be provided. Monte Carlo simulation can be used to calculate the premium and premium reserve by calculating the average value of the results from a number of independent trials. There are some variables that affect the calculations of premium and premium reserve, such as interest rate and its deviation, policy period and benefit. High interest rates make the premiums decrease, and the premium reserves grow towards zero. Great interest rate deviations make the difference between the premium with and without deviation tends to increase, so is the premium reserve. High benefits make the value of premiums increase and premium reserves growing away from zero. Long policy periods make the premiums and premium reserves of term and endowment insurance tend to increase, the premiums of pure endowment insurance decrease and the effect on premium reserves varies according the state, and premiums and premium reserves for deferred insurance which don’t follow a certain pattern. For whole life insurance, interest rates have the most influence. For pure endowment and deferred insurance, policy periods have the most influence. Meanwhile, for term and endowment insurance, interest rates and policy periods have the most influence, depending on the insured’s state.

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