Judul: Penentuan Premi Optimal pada Portofolio Heterogen dengan Menggunakan Pemrograman Tak Linear
Abstrak: Asuransi merupakan salah satu cara yang dapat digunakan untuk meminimumkan kerugian yang disebabkan oleh kejadian tidak terduga. Sebagai kewajiban dari keikutsertaan dalam jasa asuransi, pihak tertanggung harus membayar sejumlah premi yang disepakati dengan perusahaan asuransi. Salah satu risiko yang dihadapi perusahaan asuransi yaitu jika premi yang dibayarkan tidak mencukupi pembayaran klaim yang diajukan. Oleh karena itu dalam menentukan premi, risiko tersebut perlu dipertimbangkan. Premi optimal dari suatu asuransi dapat ditentukan dengan menggunakan pemrograman tak linear. Pada portofolio heterogen yang terdiri dari sejumlah besar pemegang polis asuransi yang terbagi menjadi beberapa kelas di mana setiap pemegang polis berisiko. Untuk itu ditentukan premi optimal dengan menggunakan pemrograman tak linear. Pemrograman tak linear tersebut meliputi fungsi objektif yaitu meminimumkan jumlah beda kuadrat terboboti antara besarnya total klaim dan total premi yang dibayarkan, terhadap kendala persamaan linear yaitu tingkat risiko yang telah diberikan. Langkah pertama penentuan premi optimalnya adalah dengan menentukan titik ekstrem dari fungsi pada masalah optimasi, kemudian langkah selanjutnya adalah membuktikan bahwa titik ektrem tersebut adalah minimum dengan menggunakan matriks Hess di mana akan dibuktikan bahwa matriks Hess tersebut adalah matriks definit positif dengan menggunakan dua lema terkait matriks definit positif. Dengan langkah-langkah tersebut, maka diperoleh premi optimal untuk setiap kelas dari portofolio heterogen.
Keyword: nonlinear programming, optimal premium, heterogeneous portfolio

Judul: Penentuan Premi Optimum pada Portofolio Heterogen dengan Argumen Geometris Sederhana
Abstrak: Insurance is a process of risk transfering from insureds to insurers. Insureds pay premium as a transfered risk. Amount of premium satisfies the agreement of insureds and insurers in insurance policy. In heterogeneous portfolio, there are more than one classes based on risk level for policyholders. The risk level of each class is different. For each class, it has to be determined the optimal premium based on risk level. The determining of optimal premium is to avoid insurance company from bankrupt, but it does not incriminate policyholder. Optimal premium can be determined by using simple geometrical arguments. The method for determining premium is minimizing a weighted squared difference of the total premium and total claim. From this, we will get formula for pricing optimal premium for each class in heterogeneous portfolio. The formula can be used to determine allocations for pricing of optimal premium, which are uniform allocation, semi-uniform allocation, expected principle, and variance principle.
Keyword: simple geometrical arguments, optimal premium, heterogeneous portfolio

Judul: Morphology of the gastrointestinal tract of Bandicoot Echymipera kalubu (Marsupialia: Peroryctidae).
Abstrak: Bandicoot (Echymipera kalubu) is one of marsupial which belonging to peroryctidae as well classified as endemic in Papua Island. In Papua, that species has been commonly utilized for dishes as source of protein, and traditional medicine purposed. Therefore, it requires a conservation effort in order to provide sustainability. Biological information of E. kalubu as a baseline data was quite limited. Aim of this study was to assess morphological characteristics of the digestive tract of E. kalubu’s (Marsupialia: Peroryctidae) macroscopically, microscopically and histochemically. The study was used five of adult E. kalubu with the average of body weight was 1.16 ± 0.29 kg and length of head and body was 38.2 ± 4.76 cm. Macroscopic observation were consist of morphological characteristic and morfometric of the body and the digestive track including situs viscerum. Firstly the animals was anaesthetized by combination of 50mg/kg BB Ketamine® and 10mg/kg BB Xylazine® by IM injection. The microscopic observation was used of HE, AB pH 2.5 and PAS staining methods. The result was documented with Cannon EOS 400D and microscope facilitated with Nikon Eclipse E600 for macro- and microphotography respectively. The results were then analyzed descriptively and presenting on tables and figures. Esophagus of E. kalubu was quite long with 10.92 ± 1.97 cm in length and 0.28 cm in diameter, and located along dorsamedial tracheal tube. The stomach was located in the cranial part of the left abdominal cavity. The anterior part was adjacent to diaphragm muscle, the ventro medial was covered by liver and the lateral part by spleen. The stomach of E. kalubu was simple type with short lesser curvature. The length of greater curvature was 9.1 ± 2.2 cm dan lesser curvature was 2.1 ± 0,6 cm. The intestine was relatively short that were 77.5 ± 14.4 cm in length or about two times of the body length. About ± 1.8 cm of cranial part of small intestine was piercing of both bile duct and pancreatic duct to the duodenal mucosa. However, the small and large intestines could be distinguished by the presence of caecum that was 3.4 ± 0.68 cm in length. The mucosae of esophagus E. kalubu was consist of stratified squamous epithelium with no keratinization. At the border of esophagus and stomach, the epithelium was change abruptly to a simple columnar epithelium. The muscularis mucosae was composed of smooth muscle which tends to be thicker to the caudal. The mucus type of esophageal glands were examined in the submucosal layer. The glands were found in large number in the cranial and decreased gradually toward the caudal. The number of esophageal gland was allegedly to be related to the long size of esophagus which was necessary for lubricating of food. The muscularis externa as long as the esophagus of E. kalubu were consisted of skeletal muscle. Existence of the skeletal muscle in the whole parts of esophagus presumed that mechanical function of esophagus was dominant. The glandular stomach of E. kalubu’s was differentiated as cardiac, proper gastric (fundic) and pyloric glands region. The cardiac gland was quite narrow and found in the
Keyword: Bandicoot, Echymipera kalubu, marsupials, gastrointestinal tract