Judul: Penyelesaian Masalah Dual untuk Menentukan Premi Optimum pada Portofolio Heterogen
Abstrak: Insurance is an agreement between two parties or more in which the insurer binds himself to the insured by receiving insurance premium to give back to the insured because of possible loss that may occur. The amount of premium is arranged and endorsed by two parties in an insurance policy. The problem that the insurance company has to be faced is the possibility that the claim submitted by the insured is bigger than the premium they got from the insured. If the total claim exceeds the total premium, the company will suffer bankruptcy. In this case it needs a proper formulation that can determine the optimum premium by solving the dual problems from the problems of minimizing a weighted squared difference of the total premium and total claim. The optimum solution that has been gotten from dual problem can be used to determine the optimum premium of the heterogenenous portfolio classification. From that formulation, allocation of optimum premium can be determined for each of uniform allocation, semiuniform, the expected value principle and the variance principle.
Keyword: Bogor Agricultural University (IPB), the optimum premium, premium allocation, heterogeneous portfolio, dual problem

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: Kandungan Mineral Kalakai (Stenochlaena Palustris) yang Tumbuh pada Jenis Tanah Berbeda serta Dimasak dengan Cara Berbeda
Abstrak: Kalakai (Stenochlaena palustris) is one of the local vegetables commonly available in the Palangkaraya. Previous research states that kalakai has a relatively high content of nutrients like beta carotene, folic acid, as well as some important minerals. Local communities (Dayak people) in Central Kalimantan and surrounding used to consume kalakai, especially mothers after child-birth.Kalakai has been recognized as an important vegetable to boost milk supplies for mothers who are breast-feeding. Kalakai was unique, because it can grow on various soil types, even on nutrient-poor soil. Therefore, this research aims to determine the effect of different types of soil on the mineral content of kalakai, and influence of processing on the mineral content. The sampling was conducted at five sites with different soil. They are peaty soil, sulphate acid soils, quartz sand soil, and alluvial soil in January and February. All of the samples were given four different treatments, boiling, frying, steaming and fresh (no treatment). Samples were analyzed moisture, ash, and minerals. Analysis of mineral content using Atomic Absorption Spectrophotometer (AAS) Perkin Elmer 1100B. The type of soil affect the content of minerals in the tip of kalakai leaf. It which grown on peaty soil containing a rather high of mineral Mg, Ca, Zn, Mn, which continuously reach to 5160, 6399, 134.6, 158 ppm, while Fe, Cu, and Al with a low successive level of 117.2, 4.5, 20.5 ppm. The pH of peaty soil in this study was 6.08, allegedly still quite a lot of minerals which can be absorbed by plants. Kalakai which grown on acid-suphate soil contains high Fe and Al i.e. 336.4 and 76.4 ppm. The high micro-mineral Al and Fe in acid-sulphate soils due to soil pH is low. Kalakai grown on quartz sand soil containing high minerals Ca, Cu, and Al, namely 6299, 25.1, and 58.1 ppm, respectively, while other minerals such as Mg, Fe, Zn, and Mn were low, it implies in the amount of 4598, 65, 86.8, and 65.9 ppm, respectively. Kalakai grown on alluvial soil is found that the content of Cu quite high, i.e. 7.26 ppm, whereas Fe, Mn, and Al content were low respectively 52, 63.4, and 5.3 ppm. Relatively low mineral content on kalakai of quartz sand and alluvial soil allegedly because of the low element nutrients contained in these soil types. Results of analysis of total mineral or ash content in various ways of cooking show that kalakai has a different total mineral content. Total minerals from the lowest to the highest were kalakai cooked by boiling, frying, steaming and fresh or without treatment of cooking. Cooking process give an effect to mineral content of kalakai. The process of boiling is the highest role in decreasing Mg (21-68%), Cu (11-60%), Ca (39%) and Mn (8- 38%). Other minerals such as Zn and Fe decreased by frying in the amount of 14-37% and 9-43%, respectively. The whole minerals, except Cu, still in the recommended daily intake limit, if assumed that one portion of kalakai is 50 gram dry basis.
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