Judul: Determination of Premium on Reversionary Annuity with Two Dependent Future Lifetimes using Markov Model
Abstrak: Pada umumnya, premi untuk asuransi multilife ditentukan menggunakan asumsi saling bebas. Namun, asumsi ini tidak realistis, contohnya untuk pasangan suami istri. Tujuan dari karya ilmiah ini adalah menentukan premi tunggal bersih pada reversionary annuity dengan memperhitungkan kebergantungan masa hidup di antara pasangan suami istri menggunakan batas Frechet-Hoeffding dan model Markov, membandingkan premi tunggal bersih yang memperhitungkan kebergantungan dengan premi yang menggunakan asumsi saling bebas, serta memeriksa pengaruh nilai parameter kebergantungan terhadap premi tunggal bersih. Penghitungan didasarkan pada Tabel Mortalitas Indonesia (TMI) IV mengikuti sebaran Makeham. Hasil penghitungan menunjukkan bahwa dengan model Markov nilai premi tunggal bersih lebih rendah daripada dengan model standar yang menggunakan asumsi saling bebas. Nilai premi tunggal bersih akan menurun seiring meningkatnya nilai parameter kebergantungan masa hidup lakilaki terhadap istrinya yang masih hidup. Nilai premi tunggal bersih akan meningkat seiring meningkatnya nilai parameter kebergantungan masa hidup perempuan terhadap suaminya yang masih hidup. Nilai premi tunggal bersih akan menurun seiring meningkatnya nilai parameter kebergantungan masa hidup perempuan terhadap suaminya yang sudah meninggal., In general, premiums for multilife insurance are determined by assuming the independence of the future lifetimes of insured persons. However, this assumption is unrealistic, such as for husbands and wives. The aims of this paper are to determine the net single premium on reversionary annuity by taking into account the dependence of the future lifetimes of husbands and wives using the FrechetHoeffding bounds and Markov model, to compare the net single premium that takes into account the dependence with the premium using independent assumption, as well asto examine the effect of the value of dependence parameters on the net single premium. The calculation is based on Indonesian Mortality Table IV following the Makeham distribution. The calculation results show that with Markov model the net single premium value is lower than the standard model that assumes independence. The parameter net single premium value will decrease as the value of man’s lifetime dependency parameter towards his wife who is still alive increases. The parameter net single premium value will increase as the value of woman's lifetime dependency towards her husband who is still alive increases. The parameter net single premium value will decrease as the value of woman's lifetime dependency parameter towards her deceased husband increases.
Keyword: Frechet-Hoeffding bounds, lifetime dependency, Makeham distribution, Markov model, reversionary annuity

Judul: Calculation of Premium for Life Insurance and Life Annuity Policies when Interest Rates are Modeled Using Moving Average
Abstrak: Mengikuti program asuransi jiwa adalah suatu usaha yang dapat dilakukan untuk meminimumkan risiko keuangan yang diakibatkan oleh kematian. Ketika seseorang mengikuti program asuransi, orang tersebut memiliki kewajiban untuk membayar sejumlah uang yang disebut premi. Salah satu faktor penting yang menentukan besar premi yang harus dibayar adalah tingkat bunga yang digunakan. Penelitian ini bertujuan untuk membandingkan besar premi tunggal bersih beberapa polis asuransi jiwa dan anuitas hidup saat tingkat bunga dimodelkan dengan proses moving average dan saat tingkat bunga dimodelkan dengan model independent and identically distributed. Data yang digunakan adalah data tingkat bunga BI 7-day (Reverse) Repo Rate periode April 2016 sampai April 2021 dan Tabel Mortalitas Indonesia IV. Berdasarkan hasil penghitungan, premi tunggal bersih yang dihasilkan saat tingkat bunga dimodelkan dengan proses moving average lebih besar daripada saat dimodelkan dengan model independent and identically distributed., Joining a life insurance program is an effort that can be done to minimize the financial risk due to death. When someone joins an insurance program, that person must pay a certain amount of money so-called premium. One of the important factors that determine the amount of premium to be paid is the interest rate used. This study aims to compare the net single premium of several life insurance and life annuity policies when the interest rate is modeled using a moving average process and when the interest rate is modeled using an independent and identically distributed model. The data used are BI 7-day (Reverse) Repo Rate for the period April 2016 to April 2021 and the Indonesia Mortality Table IV. Based on the calculation, the net single premiums produced when the interest rate is modeled using a moving average process is higher than those when the interest rate is modeled using an independent and identically distributed model.
Keyword: interest rate, life annuity, life insurance, moving average, net single premium

Judul: Characterizations of low alloy steel sae 4422  plated with chromic acid (Cro3)
Abstrak: Characterizations of low alloy steel SAE 4422 plated with chromic acid (CrOrO3) was use Optical Microscopy (OM), Scanning Electron Microscopy (SEM), X-Ray Diffraction (XRD), RD),Energy Dispersive Analysis of X-Ray (EDAX), Hardness Test and Roughness Test. Microstructures analysis exhibits cracks and grain boundaries microcracks as a characteristics of chrome metal found at plating metal. Perlite and Ferrite as grains of steel found at base metal with grain boundaries around it. Phase analysis of plating metal appropriate to chrome metal with lattice constant (a) is 2.559 Å and phase analysis of base metal appropriate to iron ferrite with lattice constant (a) is 3.318 Å. Both plating and base metal have cubic system. Chemical analysis of plating metal at surface section exhibits that cracks area have highest value of carbon element compare with grains and grains boundaries area. While chemical analysis of base metal at cross section exhibits that perlite have highest value of carbon element compare with ferrite and grain boundaries. The hardness value of plating metal at surface section and cross section are 753 and 637 VHN. While, the hardness value of base metal and interface area at cross section are 205 and 373 VHN. The roughness value at measurement points of chrome surface for as received sample are 0.445 μm. Observation used Optical Microscopy and Scanning Electron Microscopy exhibits surface irregularities combine to form surface texture of plating metal at surface section.
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