Agung Prabowo - Academia.edu (original) (raw)

Papers by Agung Prabowo

Jurnal Matematika Sains dan Teknologi, 2022

Dalam Kalender Jawa (Anno Javanica) terdapat dua jenis nama hari yaitu hari saptawara dan pancawa... more Dalam Kalender Jawa (Anno Javanica) terdapat dua jenis nama hari yaitu hari saptawara dan pancawara. Pancawara merupakan siklus lima hari sekali (Legi, Paing, Pon, Wage dan Kliwon). Saptawara merupakan siklus tujuh hari sekali, seperti siklus mingguan pada Kalender Gregorian (Senin, Selasa, Rabu, Kamis, Jumat, Sabtu dan Minggu). Kalender Gregorian tidak mengenal siklus pancawara. Namun, penggunaan Kalender Gregorian di Indonesia menggabungkan siklus tujuh hari dengan siklus lima hari sehingga terdapat nama hari Senin-Legi, Selasa-Paing dan seterusnya. Hasilnya adalah kombinasi 35 hari yang disebut selapanan. Dengan metode kajian pustaka, akan dibangun model matematika untuk menentukan nama hari saptawara, pancawara dan selapanan untuk tanggal tertentu pada Kalender Gregorian. Selanjutnya, model-model matematika tersebut akan dinamakan model saptawara (empat model), model pancawara dan model selapanan (masing-masing dua model).

International Journal of Ethno-Sciences and Education Research, 2022

The Rajaban tradition is a tradition of religious rituals as an expression of gratitude and momen... more The Rajaban tradition is a tradition of religious rituals as an expression of gratitude and moments to commemorate historical events, one of which is the change in the direction of Qibla from Baitul Maqdis to the Kaaba in Mecca. Based on these problems, in this article, it is shown by using the study of Graph Theory, namely the eccentric digraph to determine the center of the earth's region. Data processing is done by making the Kaaba and the seven continents on the earth's surface as a point on graph G and the side connecting the points is the distance (in km) with physical boundaries between them being considered non-existent. The results of the discussion show that the Kaaba in Mecca is the center of the earth's area with ec(v1) = 12,039 = rad(G).

International Journal of Ethno-Sciences and Education Research, 2022

In this study, mathematical concepts are used to explore the existence of mathematics in culture,... more In this study, mathematical concepts are used to explore the existence of mathematics in culture, especially in the Tasikmalaya group of geulis. By observing the current conditions, the activity of making kelom geulis is seen as a "mathematical-free" activity. It is still rare and there is still a lack of public knowledge about ethnomathematics which colors the activities of making kelom geulis as a motivation to investigate the mathematical knowledge contained in it. In addition, with the decreasing number of kelom geulis craftsmen as a result of the use of kelom geulis left by the original community producing these products. This study aims to determine and describe the ethnomathematics of the geulis group. The method used is qualitative with ethnographic methods. The subjects in this study were selected using a purposive sampling method with the research subject being a kelom geulis craftsman in the Tamansari (Gobras) area, Mulyasari, Tasikmalaya. Data collection techni...

Artikel yang ditulis oleh dosen UBAYA. MENINGKATKAN DAYA SAING PABRIK GULA DI INDONESIA ERA MASYA... more Artikel yang ditulis oleh dosen UBAYA. MENINGKATKAN DAYA SAING PABRIK GULA DI INDONESIA ERA MASYARAKAT EKONOMI ASEAN ini pada dasarnya ditujukan untuk mahasiswa Fakultas Bisnis dan Ekonomika di seluruh Indonesia. Tetapi dengan pembahasan yang sederhana dan mudah dipahami membuat artikel ini juga bisa dijadikan bacaan yang cukup bagus untuk masyarakat umum yang ingin mempelajari daya saing pabrik gula.

International Journal of Business, Economics, and Social Development, 2020

This study aims to calculate the minimum estimate of saving stocks per month to be financially fr... more This study aims to calculate the minimum estimate of saving stocks per month to be financially free after 30 years of investing in stocks. The research method used is a quantitative method. The results showed that the estimated minimum funds to get passive income of 5 million, which is equivalent for the next 30 years, is IDR 930,936 per month.

Mereka memiliki pedoman tersendiri dalam menentukan awal Ramadhan (puasa) dan awal Syawal (Hari R... more Mereka memiliki pedoman tersendiri dalam menentukan awal Ramadhan (puasa) dan awal Syawal (Hari Raya Idul Fitri). Selisih antara awal Ramadhan dan Awal Syawal menyatakan lamanya puasa Ramadhan yang harus dijalani oleh penganut Islam Aboge. Secara matematis, dapat ditunjukkan bahwa penganut Islam Aboge selamanya akan berpuasa Ramadhan selama 30 hari. Kata Kunci: aboge, cikakak, lama puasa, mathematical model, Ramadhan. Abstrack Indigenous Village Community Cikakak, Wangon subdistrict, Banyumas, Central Java Province, known as the followers of Islam Aboge (Alif Rebo Wage). They have their own guidelines in determining the start of Ramadan and the beginning of Shawwal (Eid al-Fitr). The difference between the beginning of Ramadan and the beginning of Shawwal stated duration of Ramadan that must be endured by adherents of Islam Aboge. Mathematically, it can be shown that Aboge Islamic Community will forever Ramadan fasting for 30 days.

Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), Jun 26, 2015

<jats:p>This article discusses Pawukon Saka which is a mathematical calendar.This article e... more <jats:p>This article discusses Pawukon Saka which is a mathematical calendar.This article explains mathematical knowledge required to create Pawukon Saka and particularly called as Javanese Mathematics. The Pawukon Saka Calendar obtained is then used to check some calendars sculpted on various epigraphs using The Chinese Remainder Problem. There are some mistakes in the names of wuku sculpted on some epigraphs after checking.</jats:p>

Mathematical philosophy doesn't add a number of new mathematical theorems or teories, so math... more Mathematical philosophy doesn't add a number of new mathematical theorems or teories, so mathematical phylosophy is not mathematics. Mathematical phylosophy is a reflection on mathematics. After having studied for a long time, one need to reflect the result of the study by reflecting it to mathematical phylosophy. This article discusses the mathematical phylosophy streams and their role and function, and describes formalism mathematical phylosophy specially. 1. Pendahuluan Pada masa sebelum adanya filsafat matematika, untuk mengatasi terjadinya kontradiksi salah satu caranya adalah dengan melenyapkan subyek penyebab terjadinya kontradiksi tersebut. Agar filsafat Pythagoras all is number tetap suci dan terjaga, maka Hippasus, sebagai penemu 2 yang merupakan bilangan irasional dan potensial untuk merusak filsafat Pythagoras, perlu untuk dibiarkan menjemput maut di tengah laut. Kontradiksi yang dimuculkan Hippasus dalam sistem bilangan rasioal yang dibangun Pythagoras, saat ini tid...

International Journal of Ethno-Sciences and Education Research, 2021

Serat Centhini (Suluk Tambanglaras or Suluk Tambangraras-Amongraga) is one of the greatest litera... more Serat Centhini (Suluk Tambanglaras or Suluk Tambangraras-Amongraga) is one of the greatest literary works in New Javanese literature. Its construction began in 1742 Java (1814 AD) during Sunan Pakubuwana IV. The main reference is the Jatiswara book which was made in 1711 Java or 1783 AD during Sunan Pakubuwana III. This article tracks the arithmetic information contained in Serat Centhini, including cardinal numbers, ordinal numbers, Javanese calendar, and candrasengkala. The research was carried out by using the literature study method of Serat Centhini which is translated into Indonesian and transliterated in Latin script. The results showed that Serat Centhini recorded quite a lot of mathematical information which was used in the daily life of Javanese people. The results of this study can be used as teaching materials for ethnomathematics.

Engineering Letters, 2020

This paper studies the optimal reinsurance and investment problem for insurance companies (insure... more This paper studies the optimal reinsurance and investment problem for insurance companies (insurers) with a fractional power utility function. Assuming that the insurer surplus process is approximated by Brownian motion with drift, the insurer may purchase reinsurance and invest the capital in a financial market consisting of risk-free asset and risk asset whose price is modeled by constant elasticity variance (CEV) model. The insurer’s objective is to maximize the expected fractional power utility from terminal wealth. The explicit expressions for optimal reinsurance-investment strategy and value function are determined by the stochastic approach, which uses the equations of Hamilton-Jacobi-Bellman. Finally, the numerical simulations are presented to show the effects of model parameters on the insurer’s optimal reinsurance and investment strategies.

The abstract should summarize the context, content and conclusions of the paper in less than 200-... more The abstract should summarize the context, content and conclusions of the paper in less than 200-300 words. It should not contain any references or displayed equations. Typeset the abstract in 10pt Times Roman. A maximum of 4-6 key words or phrases must be given that will be useful for retrieval and indexing. The key words must be separated by commas and should not include acronyms.

Fibonacci numbers or Fibonacci sequences are numbers or sequences that are very popular in mathem... more Fibonacci numbers or Fibonacci sequences are numbers or sequences that are very popular in mathematics. In the perspective of Mathematical Demographics, Fibonacci numbers represent the number of populations of rabbit pairs at any time. We consider this population as a hypothetical population with unlimited growth. We observe the population structure based on the phases (stages) of rabbit growth. We begin the discussion by reviewing the Fibonacci number rows in relation to the perspective of the dynamics of population systems. We analysed the hypothetical population system as a population system consisting of three age groups. Next, we build mathematical equations to produce Fibonacci numbers. The equation is built as a matrix equation, involving the growth matrix. We compiled and proved several theorems. The results of the research related to the growth matrix and its relation to the demographic bonus we describe at the end of the discussion.

International Journal of Recent Technology and Engineering

The aggregate claim model can be used to determine the amount of premium charged to the insured b... more The aggregate claim model can be used to determine the amount of premium charged to the insured by the insurance company. This model consists of two mutually independent random variables, namely the number of claims that occur per period and the amount of claim for each event. In this study, the number of claims is Poisson distributed, and the amount of claim is distributed by generalized extreme value (GEV). The Bayes method is used to estimate the parameters of each distribution. Parameter estimation results are used to calculate the expectations and variances of the aggregate claim model which are then used to calculate insurance premiums. Based on the estimation results, the amount of premium charged to the insured ranges from IDR 3,831,480 to IDR 6,443,860.

This paper tracks the history of Euclid’s fifth postulate or parallel postulate. It is a long ter... more This paper tracks the history of Euclid’s fifth postulate or parallel postulate. It is a long term postulate and dificult to be understood, and can evoke misunderstanding. Moreover, this postulate had evoked discourse among mathematicians about its dependency with other postulates for a long time untill the 19th century. The discourse related to assuredness of mathematician after Euclid’s era is whether or not Euclid’s fifth postulate can be deduced from other four postulates. But, the discourse became precisely a cause of finding of new geometry system, called non-Euclide geometry.

International Journal of Quantitative Research and Modeling

Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbe... more Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbers differ in the first term, while the second term is entirely the same. The next terms are the sum of two successive terms. In this article, generalizations of Fibonacci, Lucas and Mulatu (GFLM) numbers are built which are generalizations of the three types of numbers. The Binet formula is then built for the GFLM numbers, and determines the golden ratio, silver ratio and Bronze ratio of the GFLM numbers. This article also presents generalizations of these three types of ratios, called Metallic ratios. In the last part we state the Metallic ratio in the form of continued fraction and nested radicals.

Jurnal Matematika Sains dan Teknologi

Option is a financial instrument where price depends on the underlying stock price. The pricing o... more Option is a financial instrument where price depends on the underlying stock price. The pricing of options, both selling options and purchase options, may use the CRR (Cox-Ross-Rubinstein) binomial model. Only two possible parameters were used that is u if the stock price rises and d when the stock price down. One of the elements that determine option prices is volatility. In the binomial model CRR volatility is constant. In fact, the financial market price of stocks fluctuates so that volatility also fluctuates. This article discusses volatility of fluctuating stock price movements by modeling it using binomial fuzzy with triangular curve representation. The analysis is carried out in relation to the existence of three interpretations of the triangular curve representation resulting in different degrees of membership. In addition to volatility, this study added the size or risk level ρ. As an illustration, this study used stock price movement data from PT. Antam (Persero) from Augu...

Matematika Jawa telah eksis sejak 732 M pada masa Rakai Mataram Sang Ratu Sanjaya sehingga Matema... more Matematika Jawa telah eksis sejak 732 M pada masa Rakai Mataram Sang Ratu Sanjaya sehingga Matematika Jawa merupakan wujud kearifan lokal (local genius) yang dikembangkan masyarakat Jawa sejak 732 M hingga hari ini. Matematika Jawa digunakan sebagai pelayan ilmu (servant), bukan untuk mengembangkan Matematika Jawa itu sendiri (queen). Wujud eksistensi Matematika Jawa tersebut dapat ditemukan pada Prasasti Canggal. Dengan demikian, prasasti-prasasti dari tanah Jawa tidak hanya menjadi sumber penelitian dan penulisan sejarah, tetapi juga menjadi media untuk penelitian matematika. Tulisan ini melaporkan hasil penelitian dengan menggunakan prasasti, kitab Jawa kuno, pusara, wayang, candi dan lain-lain sebagai media atau sumber penelitian Matematika Jawa. Hasil-hasil penelitian Matematika Jawa dapat disebutkan antara lain penggunaan basis bilangan 10, bentuk-bentuk angka, lafal-lafal bilangan, lafal dan bentuk angka 0, kelipatan bilangan, modulo Jawa, operasi aritmatika, bilangan pecahan dan lain-lain. Matematika Jawa mewujud dalam bentuk yang berbeda dengan Matematika (Matematika Sekolah) yang hari ini diajarkan di sekolah-sekolah. Matematika Sekolah secara resmi pertama kali dikenal dan diajarkan sejak masa Politik Etis (Balas Budi) tahun 1901 meskipun penggunaannya telah ada sejak awal penjajahan Belanda. Jadi, bagi masyarakat Jawa eksistensi Matematika Jawa sebagai local genius jauh mendahului Matematika (Matematika Sekolah).

International Journal of Mathematics Trends and Technology

Mathematics and Statistics

Linear regression is widely used in various fields. Research on linear regression uses the OLS an... more Linear regression is widely used in various fields. Research on linear regression uses the OLS and ML method in estimating its parameters. OLS and ML method require many assumptions to complete. It is frequently found there is an unconditional assumption that both methods are not successfully used. This paper proposes a new method which does not require any assumption with a condition. The new method is called SAM (Simple Averaging Method) to estimate parameters in the simple linear regression model. The method may be used without fulfilling assumptions in the regression model. Three new theorems are formulated to simplify the estimation of parameters in the simple linear regression model with SAM. By using the same data, the simple linear regression model parameter estimation is conducted using SAM. The result shows that the obtained regression parameter is not quite far different. However, to measure the accuracy of both methods, a comparison of errors made by each method is conducted using Root Mean Square Error (RMSE) and Mean Averaged Error (MAE). By comparing the values of RMSE and MAE for both methods, SAM method may be used to estimate parameters in the regression equation. The advantage of SAM is free from all assumptions required by regression, such as error normality assumption while the data should be from the normal distribution.

Jurnal Matematika Sains dan Teknologi, 2022

Dalam Kalender Jawa (Anno Javanica) terdapat dua jenis nama hari yaitu hari saptawara dan pancawa... more Dalam Kalender Jawa (Anno Javanica) terdapat dua jenis nama hari yaitu hari saptawara dan pancawara. Pancawara merupakan siklus lima hari sekali (Legi, Paing, Pon, Wage dan Kliwon). Saptawara merupakan siklus tujuh hari sekali, seperti siklus mingguan pada Kalender Gregorian (Senin, Selasa, Rabu, Kamis, Jumat, Sabtu dan Minggu). Kalender Gregorian tidak mengenal siklus pancawara. Namun, penggunaan Kalender Gregorian di Indonesia menggabungkan siklus tujuh hari dengan siklus lima hari sehingga terdapat nama hari Senin-Legi, Selasa-Paing dan seterusnya. Hasilnya adalah kombinasi 35 hari yang disebut selapanan. Dengan metode kajian pustaka, akan dibangun model matematika untuk menentukan nama hari saptawara, pancawara dan selapanan untuk tanggal tertentu pada Kalender Gregorian. Selanjutnya, model-model matematika tersebut akan dinamakan model saptawara (empat model), model pancawara dan model selapanan (masing-masing dua model).

International Journal of Ethno-Sciences and Education Research, 2022

The Rajaban tradition is a tradition of religious rituals as an expression of gratitude and momen... more The Rajaban tradition is a tradition of religious rituals as an expression of gratitude and moments to commemorate historical events, one of which is the change in the direction of Qibla from Baitul Maqdis to the Kaaba in Mecca. Based on these problems, in this article, it is shown by using the study of Graph Theory, namely the eccentric digraph to determine the center of the earth's region. Data processing is done by making the Kaaba and the seven continents on the earth's surface as a point on graph G and the side connecting the points is the distance (in km) with physical boundaries between them being considered non-existent. The results of the discussion show that the Kaaba in Mecca is the center of the earth's area with ec(v1) = 12,039 = rad(G).

International Journal of Ethno-Sciences and Education Research, 2022

In this study, mathematical concepts are used to explore the existence of mathematics in culture,... more In this study, mathematical concepts are used to explore the existence of mathematics in culture, especially in the Tasikmalaya group of geulis. By observing the current conditions, the activity of making kelom geulis is seen as a "mathematical-free" activity. It is still rare and there is still a lack of public knowledge about ethnomathematics which colors the activities of making kelom geulis as a motivation to investigate the mathematical knowledge contained in it. In addition, with the decreasing number of kelom geulis craftsmen as a result of the use of kelom geulis left by the original community producing these products. This study aims to determine and describe the ethnomathematics of the geulis group. The method used is qualitative with ethnographic methods. The subjects in this study were selected using a purposive sampling method with the research subject being a kelom geulis craftsman in the Tamansari (Gobras) area, Mulyasari, Tasikmalaya. Data collection techni...

Artikel yang ditulis oleh dosen UBAYA. MENINGKATKAN DAYA SAING PABRIK GULA DI INDONESIA ERA MASYA... more Artikel yang ditulis oleh dosen UBAYA. MENINGKATKAN DAYA SAING PABRIK GULA DI INDONESIA ERA MASYARAKAT EKONOMI ASEAN ini pada dasarnya ditujukan untuk mahasiswa Fakultas Bisnis dan Ekonomika di seluruh Indonesia. Tetapi dengan pembahasan yang sederhana dan mudah dipahami membuat artikel ini juga bisa dijadikan bacaan yang cukup bagus untuk masyarakat umum yang ingin mempelajari daya saing pabrik gula.

International Journal of Business, Economics, and Social Development, 2020

This study aims to calculate the minimum estimate of saving stocks per month to be financially fr... more This study aims to calculate the minimum estimate of saving stocks per month to be financially free after 30 years of investing in stocks. The research method used is a quantitative method. The results showed that the estimated minimum funds to get passive income of 5 million, which is equivalent for the next 30 years, is IDR 930,936 per month.

Mereka memiliki pedoman tersendiri dalam menentukan awal Ramadhan (puasa) dan awal Syawal (Hari R... more Mereka memiliki pedoman tersendiri dalam menentukan awal Ramadhan (puasa) dan awal Syawal (Hari Raya Idul Fitri). Selisih antara awal Ramadhan dan Awal Syawal menyatakan lamanya puasa Ramadhan yang harus dijalani oleh penganut Islam Aboge. Secara matematis, dapat ditunjukkan bahwa penganut Islam Aboge selamanya akan berpuasa Ramadhan selama 30 hari. Kata Kunci: aboge, cikakak, lama puasa, mathematical model, Ramadhan. Abstrack Indigenous Village Community Cikakak, Wangon subdistrict, Banyumas, Central Java Province, known as the followers of Islam Aboge (Alif Rebo Wage). They have their own guidelines in determining the start of Ramadan and the beginning of Shawwal (Eid al-Fitr). The difference between the beginning of Ramadan and the beginning of Shawwal stated duration of Ramadan that must be endured by adherents of Islam Aboge. Mathematically, it can be shown that Aboge Islamic Community will forever Ramadan fasting for 30 days.

Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), Jun 26, 2015

<jats:p>This article discusses Pawukon Saka which is a mathematical calendar.This article e... more <jats:p>This article discusses Pawukon Saka which is a mathematical calendar.This article explains mathematical knowledge required to create Pawukon Saka and particularly called as Javanese Mathematics. The Pawukon Saka Calendar obtained is then used to check some calendars sculpted on various epigraphs using The Chinese Remainder Problem. There are some mistakes in the names of wuku sculpted on some epigraphs after checking.</jats:p>

Mathematical philosophy doesn't add a number of new mathematical theorems or teories, so math... more Mathematical philosophy doesn't add a number of new mathematical theorems or teories, so mathematical phylosophy is not mathematics. Mathematical phylosophy is a reflection on mathematics. After having studied for a long time, one need to reflect the result of the study by reflecting it to mathematical phylosophy. This article discusses the mathematical phylosophy streams and their role and function, and describes formalism mathematical phylosophy specially. 1. Pendahuluan Pada masa sebelum adanya filsafat matematika, untuk mengatasi terjadinya kontradiksi salah satu caranya adalah dengan melenyapkan subyek penyebab terjadinya kontradiksi tersebut. Agar filsafat Pythagoras all is number tetap suci dan terjaga, maka Hippasus, sebagai penemu 2 yang merupakan bilangan irasional dan potensial untuk merusak filsafat Pythagoras, perlu untuk dibiarkan menjemput maut di tengah laut. Kontradiksi yang dimuculkan Hippasus dalam sistem bilangan rasioal yang dibangun Pythagoras, saat ini tid...

International Journal of Ethno-Sciences and Education Research, 2021

Serat Centhini (Suluk Tambanglaras or Suluk Tambangraras-Amongraga) is one of the greatest litera... more Serat Centhini (Suluk Tambanglaras or Suluk Tambangraras-Amongraga) is one of the greatest literary works in New Javanese literature. Its construction began in 1742 Java (1814 AD) during Sunan Pakubuwana IV. The main reference is the Jatiswara book which was made in 1711 Java or 1783 AD during Sunan Pakubuwana III. This article tracks the arithmetic information contained in Serat Centhini, including cardinal numbers, ordinal numbers, Javanese calendar, and candrasengkala. The research was carried out by using the literature study method of Serat Centhini which is translated into Indonesian and transliterated in Latin script. The results showed that Serat Centhini recorded quite a lot of mathematical information which was used in the daily life of Javanese people. The results of this study can be used as teaching materials for ethnomathematics.

Engineering Letters, 2020

This paper studies the optimal reinsurance and investment problem for insurance companies (insure... more This paper studies the optimal reinsurance and investment problem for insurance companies (insurers) with a fractional power utility function. Assuming that the insurer surplus process is approximated by Brownian motion with drift, the insurer may purchase reinsurance and invest the capital in a financial market consisting of risk-free asset and risk asset whose price is modeled by constant elasticity variance (CEV) model. The insurer’s objective is to maximize the expected fractional power utility from terminal wealth. The explicit expressions for optimal reinsurance-investment strategy and value function are determined by the stochastic approach, which uses the equations of Hamilton-Jacobi-Bellman. Finally, the numerical simulations are presented to show the effects of model parameters on the insurer’s optimal reinsurance and investment strategies.

The abstract should summarize the context, content and conclusions of the paper in less than 200-... more The abstract should summarize the context, content and conclusions of the paper in less than 200-300 words. It should not contain any references or displayed equations. Typeset the abstract in 10pt Times Roman. A maximum of 4-6 key words or phrases must be given that will be useful for retrieval and indexing. The key words must be separated by commas and should not include acronyms.

Fibonacci numbers or Fibonacci sequences are numbers or sequences that are very popular in mathem... more Fibonacci numbers or Fibonacci sequences are numbers or sequences that are very popular in mathematics. In the perspective of Mathematical Demographics, Fibonacci numbers represent the number of populations of rabbit pairs at any time. We consider this population as a hypothetical population with unlimited growth. We observe the population structure based on the phases (stages) of rabbit growth. We begin the discussion by reviewing the Fibonacci number rows in relation to the perspective of the dynamics of population systems. We analysed the hypothetical population system as a population system consisting of three age groups. Next, we build mathematical equations to produce Fibonacci numbers. The equation is built as a matrix equation, involving the growth matrix. We compiled and proved several theorems. The results of the research related to the growth matrix and its relation to the demographic bonus we describe at the end of the discussion.

International Journal of Recent Technology and Engineering

The aggregate claim model can be used to determine the amount of premium charged to the insured b... more The aggregate claim model can be used to determine the amount of premium charged to the insured by the insurance company. This model consists of two mutually independent random variables, namely the number of claims that occur per period and the amount of claim for each event. In this study, the number of claims is Poisson distributed, and the amount of claim is distributed by generalized extreme value (GEV). The Bayes method is used to estimate the parameters of each distribution. Parameter estimation results are used to calculate the expectations and variances of the aggregate claim model which are then used to calculate insurance premiums. Based on the estimation results, the amount of premium charged to the insured ranges from IDR 3,831,480 to IDR 6,443,860.

This paper tracks the history of Euclid’s fifth postulate or parallel postulate. It is a long ter... more This paper tracks the history of Euclid’s fifth postulate or parallel postulate. It is a long term postulate and dificult to be understood, and can evoke misunderstanding. Moreover, this postulate had evoked discourse among mathematicians about its dependency with other postulates for a long time untill the 19th century. The discourse related to assuredness of mathematician after Euclid’s era is whether or not Euclid’s fifth postulate can be deduced from other four postulates. But, the discourse became precisely a cause of finding of new geometry system, called non-Euclide geometry.

International Journal of Quantitative Research and Modeling

Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbe... more Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbers differ in the first term, while the second term is entirely the same. The next terms are the sum of two successive terms. In this article, generalizations of Fibonacci, Lucas and Mulatu (GFLM) numbers are built which are generalizations of the three types of numbers. The Binet formula is then built for the GFLM numbers, and determines the golden ratio, silver ratio and Bronze ratio of the GFLM numbers. This article also presents generalizations of these three types of ratios, called Metallic ratios. In the last part we state the Metallic ratio in the form of continued fraction and nested radicals.

Jurnal Matematika Sains dan Teknologi

Option is a financial instrument where price depends on the underlying stock price. The pricing o... more Option is a financial instrument where price depends on the underlying stock price. The pricing of options, both selling options and purchase options, may use the CRR (Cox-Ross-Rubinstein) binomial model. Only two possible parameters were used that is u if the stock price rises and d when the stock price down. One of the elements that determine option prices is volatility. In the binomial model CRR volatility is constant. In fact, the financial market price of stocks fluctuates so that volatility also fluctuates. This article discusses volatility of fluctuating stock price movements by modeling it using binomial fuzzy with triangular curve representation. The analysis is carried out in relation to the existence of three interpretations of the triangular curve representation resulting in different degrees of membership. In addition to volatility, this study added the size or risk level ρ. As an illustration, this study used stock price movement data from PT. Antam (Persero) from Augu...

Matematika Jawa telah eksis sejak 732 M pada masa Rakai Mataram Sang Ratu Sanjaya sehingga Matema... more Matematika Jawa telah eksis sejak 732 M pada masa Rakai Mataram Sang Ratu Sanjaya sehingga Matematika Jawa merupakan wujud kearifan lokal (local genius) yang dikembangkan masyarakat Jawa sejak 732 M hingga hari ini. Matematika Jawa digunakan sebagai pelayan ilmu (servant), bukan untuk mengembangkan Matematika Jawa itu sendiri (queen). Wujud eksistensi Matematika Jawa tersebut dapat ditemukan pada Prasasti Canggal. Dengan demikian, prasasti-prasasti dari tanah Jawa tidak hanya menjadi sumber penelitian dan penulisan sejarah, tetapi juga menjadi media untuk penelitian matematika. Tulisan ini melaporkan hasil penelitian dengan menggunakan prasasti, kitab Jawa kuno, pusara, wayang, candi dan lain-lain sebagai media atau sumber penelitian Matematika Jawa. Hasil-hasil penelitian Matematika Jawa dapat disebutkan antara lain penggunaan basis bilangan 10, bentuk-bentuk angka, lafal-lafal bilangan, lafal dan bentuk angka 0, kelipatan bilangan, modulo Jawa, operasi aritmatika, bilangan pecahan dan lain-lain. Matematika Jawa mewujud dalam bentuk yang berbeda dengan Matematika (Matematika Sekolah) yang hari ini diajarkan di sekolah-sekolah. Matematika Sekolah secara resmi pertama kali dikenal dan diajarkan sejak masa Politik Etis (Balas Budi) tahun 1901 meskipun penggunaannya telah ada sejak awal penjajahan Belanda. Jadi, bagi masyarakat Jawa eksistensi Matematika Jawa sebagai local genius jauh mendahului Matematika (Matematika Sekolah).

International Journal of Mathematics Trends and Technology

Mathematics and Statistics

Linear regression is widely used in various fields. Research on linear regression uses the OLS an... more Linear regression is widely used in various fields. Research on linear regression uses the OLS and ML method in estimating its parameters. OLS and ML method require many assumptions to complete. It is frequently found there is an unconditional assumption that both methods are not successfully used. This paper proposes a new method which does not require any assumption with a condition. The new method is called SAM (Simple Averaging Method) to estimate parameters in the simple linear regression model. The method may be used without fulfilling assumptions in the regression model. Three new theorems are formulated to simplify the estimation of parameters in the simple linear regression model with SAM. By using the same data, the simple linear regression model parameter estimation is conducted using SAM. The result shows that the obtained regression parameter is not quite far different. However, to measure the accuracy of both methods, a comparison of errors made by each method is conducted using Root Mean Square Error (RMSE) and Mean Averaged Error (MAE). By comparing the values of RMSE and MAE for both methods, SAM method may be used to estimate parameters in the regression equation. The advantage of SAM is free from all assumptions required by regression, such as error normality assumption while the data should be from the normal distribution.