Judul: Peluang Kebangkrutan Perusahaan Asuransi saat Banyaknya Klaim Mengikuti Proses Binomial
Abstrak: Pada model risiko klasik, keuntungan dalam perusahaan asuransi adalah proses akumulasi kekayaan yang dipengaruhi oleh jumlah modal awal, besarnya total pendapatan (premi) yang masuk, dan akumulasi klaim yang harus dibayarkan perusahaan kepada para pemegang polis. Perusahaan asuransi dikatakan bangkrut jika keuntungan perusahaan bernilai negatif, yaitu ketika besar modal awal ditambah total penerimaan premi lebih kecil dari besar akumulasi klaim yang harus dibayarkan. Pada penelitian ini direkonstruksi peluang kebangkrutan perusahaan asuransi saat banyaknya klaim mengikuti proses binomial. Selain itu, diberikan pula ilustrasi proses keuntungannya. Berdasarkan ilustrasi tersebut, didapatkan bahwa peluang kebangkrutan berbanding terbalik dengan modal awal dan berbanding lurus dengan peluang terjadinya klaim.
Keyword: binomial process, insurance, probability of ruin

Judul: Penentuan peluang kebangrutan perusahaan asuransi dari peluang survival
Abstrak: Model matematika dalam perusahaan asuransi banyak dipergunakan untuk menganalisa masalah asuransi. Salah satu permasalahan perusahaan asuransi yang dibahas dalam karya ilmiah ini adalah menentukan peluang kebangkrutan perusahaan asuransi dalam model waktu diskrit dan kontinu. Untuk memperoleh peluang kebangkrutan secara langsung sangat sulit, maka dilakukan pendekatan dengan mencari peluang survival, yang merupakan lawan dari peluang kebangkrutan. Peluang survival adalah peluang yang surplusnya selalu tak negatif dan sangat bergantung pada surplus awal. Dalam menyelesaikan masalah peluang kebangkrutan model waktu diskrit digunakan proses random walk, sedangkan untuk menyelesaikan peluang kebangkrutan model waktu kontinu digunakan proses Poisson. Hasil akhir yang diperoleh dari pencarian peluang survival inilah yang akan menentukan peluang kebangkrutan bagi perusahaan asuransi yang bersangkutan. Untuk model waktu diskrit, peluang survival diperoleh secara rekursif sebagai berikut: R(u) = R(u+z).v(3) u = 0, 1, 2, ... -1 dengan R(0) = 1 + Σ ZV(E) P(1) Sedangkan untuk model waktu kontinu, diperoleh peluang survival sebagai berikut: 00 R(u) = She λt de [R(u+ct− s)dP(s), 0 dengan R(0) 1-2µ/c.
Keyword: 

Judul: Utilization of hydrolized duckweed (Lemna minor) meal as a soybean replacement in Nile tilapia (Oreochromis niloticus) diet,
Abstrak: Tilapia is a fast growing fish widely cultured in many tropical and sub tropical countries. The recent production figures reported our global production estimates for 2015 is 5,576.8 metric tons. In developing countries the major challenges facing aquaculture industry is high cost of production associated with fish feeds. Feed represents 40-70% of operating costs for aquaculture operations, increasing expenses and potential declining supplies soybean meal have led scientists to search for less expensive but compatible alternative protein sources for fish feed; most of which are based on animal or plant protein sources. The objectives of study was to determine the incubation period for hydrolysis of duckweed and to evaluate the use of hydrolized duckweed as aprotein source for the growth performance of Nile tilapia Three experiments were conducted to determine the composition and digestibility of hydrolyzed duckweed meal by sheep rumen liquor as the replacement of soybean meal in the diet of Nile tilapia. The first trial examined the effectivity of sheep rumen liquor enzyme to decrease crude fiber contents of (DWM), the added volume of sheep rumen liquor was 100 ml/kg DWM and then it was incubated for 0, 12, 24 hr . The second trial was to evaluate the apparent digestibility of hydrolyzed DWM for Nile Tilapia, apparent digestibility were determined using chromic oxide indicator added to both reference diet and test diets. The feed ingredients used in the trial were hydrolyzed DWM (HDWM) and unhydrolyzed DWM (DWM). Ten fish with an average weight of 18±0.36g were used in the trial and reared in the aquarium of size 30×40×50cm for 15 days; feces were collected from three replicates using a fecal collection column attached to the aquarium. Third trial was to evaluate the growth performance of Tilapia fed test diet with hydrolyzed Duckweed meal (HDWM). The experimental design was set according to completely randomized design with four treatments and three replicates of HDWM inclusion levels that is 0%, 15%, 30% and 45%. Nile tilapia fish with initial body weight of 18±0.36g was kept in 12 units aquarium size of 30×40×50cm at stocking density of 10fish/aquarium, the fish were fed two times a day at 08:00am and 16:00pm to apparent satiation for a period of 60 days. The results indicated that duckweed meal (DWM) hydrolyzed with 100 mL/kg and incubated for 24 hrs showed the lowest crude fiber contents of 13.68% compared to other treatments. Total digestibility of hydrolyzed duckweed (HDWM) meal was 87.3% compared with unhydrolyzed duckweed (DWM) which was 66.8%. Total final weight (TFW), survival rate (SR), specific growth rate (SGR), feed conversional rate (FCR) and protein retention (PR) shows growth performance at 15% inclusion. The results of this study showed that 100mL/kg sheep rumen liquor at incubation period of 24 hr can be suitable for hydrolysis of duckweed to reduce crude fiber also hydrolyzed duckweed can substitute soybean meal at an incubation rate of 15% in the diet of Nile tilapia and had the same growth and FCR with control diet
Keyword: Digestibility, Duckweed meal, Growth performance, Sheep rumen