Judul: Penentuan Harga Premi, Fungsi Permintaan, dan Kesetimbangannya pada Portfolio Heterogen
Abstrak: A heterogenous portfolio is a collection of insureds, which can be grouped into several risk classes. The insurer determines premium pricing in each risk class, using a certain pricing function. Pricing function is a function that states the amount of the premium based on the number of insured in each class. Each class has its own demand function, which determines the number of insured in this class as a function of the premium. This thesis aims to study the interaction between the number of insured in each class of a heterogenous portfolio and its premium. First, the insurer determines the premiums based on some initial number of insured in each class. Then, market reacts by updating the number of the policyholders. As a consequence, the insurer updates the premium. This process repeats until a certain condition is satisfied. This process has been proved to have an equilibrium point. The characteristics of the equilibrium point are determined by the fixed-point theorem. Finally, to illustrate the theory, the calculation of premium based on a demand function in equilibrium point for five risk classes is applied using Mathematica software.
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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: In vitro propagation and micro bulb induction of shallot
Abstrak: Shallot growers use harvested bulbs as propagules for the next planting. The use of the bulbs may cause degenerative diseases. Therefore, propagation system of shallot must be sought. A series of experiments were conducted in the Department of Agronomy and Horticulture IPB and the University of Queensland from May 2007 to July 2011. The first objective in this experiment was to determine the effect of explant storage duration on in vitro shoot multiplication of shallot. The experimental results showed storage length affected the growth of culture. Twomonth stored bulbs gave the best results on the number of micro shoots, number of leaves and roots and less vitrification. Four-week-old shoots were the best used for micro-propagules in shallot micro bulb induction. The objective of the second experiment was to determine the effect of temperature on the formation of shallot micro bulbs. It was shown that room temperature influenced the number of micro bulb, bulb base diameter, the widest diameter, ratio of the widest diameter and the base diameter of shallot micro bulb (Dt / Dp), root length, shoot length, number of leaves, number of senescing leaf. Temperature of 30/27 °C was better than 20/17 oC in accelerating the process of micro-bulb formation and increased the size of shallot micro bulbs. The objective of the third experiment was to determine the effect of sucrose and paclobutrazol on micro bulb induction. No interaction between sucrose and paclobutrazol was shown. Sucrose affected plant height, number of senescing leaf, root number, root length, the weight of plantlets and micro bulb widest diameter. Sucrose concentration of 90 g L-1 was the best in inducing shallot micro bulbs. Paclobutrazol significantly affected plant height, number of senescing leaf, number and length of roots. Paclobutrazol at level 10 mg L-1 inhibited plant height, leaf number and root length. Paclobutrazol 0.1-10 mg L-1 shortened root length. Paclobutrazol at concentration of 1 and 10 mg L-1 produced an abnormal form of micro bulb. The objective of the fourth experiment was to determine the success of shallot shoot and micro bulb acclimatization. At this stage of acclimatization, micro bulbs could be successfully grown for 3 weeks after acclimatization. Micro bulb was better in acclimatization than rooted plantlet. Plants may be transplanted to the field at 2 weeks after acclimatization. It is concluded that bulb stored for two months was the best for shoot multiplication. Media MS+vit B5 and 90 g L-1 sucrose at 30 oC was the best for bulb induction. Paclobutrazol should not be used for bulb induction. Bulb was better acclimatized than planlet. The media for acclimatization was green leaf compost and husk charcoal.
Keyword: Allium ascalonicum L, micro bulb, explant age, room temperature, paclobutrazol