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INDONESIA
Epsilon: Jurnal Matematika Murni dan Terapan
Published by Universitas Lambung Mangkurat
ISSN : 19784422     EISSN : 26567660     DOI : http://dx.doi.org/10.20527
Core Subject : Science, Engineering,
Decision Sciences, Operations Research & Management Transportation
Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational Mathematics
Arjuna Subject : Matematika - Matematika Terapan
Articles 220 Documents
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ANALISIS VALUE AT RISK PADA PORTOFOLIO OPTIMAL SAHAM BLUE CHIP DENGAN METODE RESAMPLED EFFICIENT FRONTIER Febryanti, Winda; Sulistianingsih, Evy; Kusnandar, Dadan
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.10170

Abstract

Investor sudah seharusnya memperhatikan strategi dalam berinvestasi guna mencapai hasil return tertentu dengan risiko yang sekecil mungkin. Strategi investasi untuk meningkatkan return dengan risiko minimum yaitu pembentukan portofolio dengan metode Resampled Efficient Frontier (REF). Metode REF adalah cara yang digunakan untuk mengatasi ketidakstabilan MVEP dengan memanfaatkan simulasi Monte Carlo yang kemudian membentuk portofolio efisien yang berbeda dan  dihitung rata-ratanya guna menghasilkan REF. Penelitian ini menganalisis perhitungan Value at Risk (VaR) pada portofolio optimal menggunakan metode REF. Penelitian ini menggunakna data sekunder harga penutupan saham harian BBRI dan BBNI periode 28 Oktober 2021-28 Oktober 2022 sebanyak 246 hari. Data return saham BBRI dan BBNI dibangkitkan sebanyak 1000 simulasi dengan 51 titik efisien. Pada tingkat kepercayaan 95% dengan periode investasi satu hari, menghasilkan nilai VaR yang berbeda-beda untuk setiap tingkat risiko portofolio. Berdasarkan hasil perhitungan VaR dengan metode REF diperoleh nilai VaR sebesar Rp2.446.277,00 untuk portofolio berisiko minimum, Rp2.496.548,00 untuk risiko sedang dan Rp2.590.817,00 untuk risiko maksimum.
SIFAT ELEMENTER DARI RING TERGENERALISASI Rosyadi, Gusti Muhammad; Hijriati, Na'imah
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12619

Abstract

Ring is a study of algebraic structures, which is defined as a non-empty set containing two binary operations. Regarding the first binary operation, the set is a group, and the second binary operation is a semigroup, and both operations fulfill the left distributive and right distributive properties. The generalized ring concept is an extension of the ring concept, namely that for the first binary operation, each element has an identity element that is not necessarily the same. This research aims to prove the elementary properties of generalized rings and the properties of generalized rings associated with the G-ring structure. Furthermore, this research also proves the properties of subsets related to identity elements in generalized rings. The results of this research are that the fundamental properties of the generalized ring are valid, which are analogous to the fundamental properties of the ring, and sufficient conditions for a generalized ring to be a G-ring are obtained. Furthermore, if the generalized ring has a unit element, it forms an abelian group with all elements having the same identity, and the generalized ring contains all identity elements.
APLIKASI MODEL TREND UNTUK MEMPREDIKSI PRODUKSI KELAPA SAWIT PROVINSI KALIMANTAN SELATAN Salam, Nur; Lestia, Aprida Siska; Jannah, Noor; Firdaus, Muhammad
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.10780

Abstract

The plantation sector has a large and extensive reach, one type of plantation crop that is widely cultivated in Indonesia is oil palm. Business in the oil palm plantation sector is also one of the leading potential areas in South Kalimantan Province. One of the provinces producing the most palm oil in Indonesia is South Kalimantan Province. This research is a literature study regarding predictions of palm oil production. The aim of this research is to determine the appropriate prediction model for data on the amount of palm oil (CPO) production in the South Kalimantan Province Region and to explain the results of palm oil predictions in the South Kalimantan Province Region using a trend model. The application of the trend model used in this research takes into account the error value obtained with the smallest MAPE (Mean Absolute Percentage Error). The nature of the data regarding the amount of palm oil production in the South Kalimantan Province Region from 2001 to 2021 tends to continue to increase so that the data can be predicted using trend methods, namely linear, quadratic and exponential. For the prediction results of palm oil production using the best trend model with the smallest MAPE value, namely 16% with the linear trend model: ... The predicted amounts of palm oil production from 2022 to 2027 which tend to continue to increase are: 1.336.359, 1.397.196, 1.458.032, 1.518.869, 1.579.705 and 1.640.542 tons.
MODEL INVESTASI POLIS ASURANSI JIWA BERBONUS TIPE DWIGUNA DENGAN AMERICAN PUT OPTION Lissa, Hermei; Putri, Endah R.M.
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12625

Abstract

Insurance is a form of protection against the concept of risk transfer that may occur from an uncertain event. One type of insurance is life insurance. With the changing times, life insurance launched innovative products, one of which is endowment life insurance. Endowment life insurance is a type of life insurance that provides compensation benefits if the policy holder dies during the coverage period, as well as providing cash value and bonuses if the policy holder is still alive until the end of the period. This study aims to determine the fair price of insurance policies and the price of bonus life insurance policies. Determination of the value of the American put option with the binomial method using a numerical approach, the formulation of the portfolio model includes determining the model of the unit price with Geometric Brownian Motion, solving using Black-Scholes, determining the structure of the bonus life insurance policy with the formulation of a single premium payment, bonus rate, and benefits. then analyze the movement of the price of a reasonable bonus life insurance policy with a surrender option based on the age of the insured, technical rate, participation level, and volatility. The surrender value obtained is the difference between the value of the American Put option and the European Call Option. Based on the simulation, the conclusion of this analysis is that the price of the endowment type life insurance policy can be estimated using the binomial method at around 0.78 for a fair policy price and around 0.27 for a policy price with a surrender option. This gives an idea of the relative value of the policy price to the expected benefits under certain conditions, such as the death of the insured in the first year of the contract.
KONTROL SLIDING MODE ADAPTIF DENGAN VAKSINASI DAN TREATMENT PADA MODEL PENYEBARAN TUBERKULOSIS Ayu, Regina Wahyudyah Sonata
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12326

Abstract

This research examines the design of adaptive sliding mode control in a tuberculosis (TB) disease spread model, considering uncertainties within the model. The TB model involves five state variables (susceptible individuals, vaccinated individuals, individuals with latent TB infection, individuals with active TB infection, and individuals under treatment) and three control input variables consisting of vaccination and treatment. The objective of this control design is to reduce the number of susceptible individuals, individuals with active TB infection, and the number of individuals under treatment by tracking the given reference functions. Stability and convergence of tracking errors of the controlled system are proved using the Lyapunov Stability Theorem. Numerical simulations are conducted to evaluate the performance of the designed control under various parameter uncertainty conditions. Based on the simulation results, it is shown that the adaptive sliding mode controllers guarantee the convergence of tracking errors is achieved despite the presence of uncertainty in the model.
METODE BLACK-SCHOLES DALAM PENENTUAN HARGA OPSI Taufik, Ahmad; Idris, Mochammad; Lestia, Aprida Siska
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12604

Abstract

The Black-Scholes Method is one of the option pricing method that introduced by Fischer Black and Myron Scholes in 1973. This study aim to review the determination of the price of an option with stocks as the underlying assets and based on  Black and Scholes assumptions. These assumptions lead to construct an equation named Black-Scholes differential equations, which is the equation that must be satisfied for option as the derivative instrument and non-dividend giving stocks as the underlying assets. After the Black-Scholes differential equations formed successfully, the next step is to find the solution of that equation. Consider the option is call option, the solution that will be obtained from solving the equation is the price of call option. Then substitute it to the put-call parity equation, which is the equation that shows the relationship between call and put option prices, so the price of put option can be obtained too. The estimation that obtained from the Black-Scholes method is the highest price for a contract is said to be fair and worth to buy for the holder.
PREDIKSI INDEKS HARGA KONSUMEN KELOMPOK BAHAN MAKANAN DI PROVINSI KALIMANTAN SELATAN Annisa, Selvi; Azizah, Rahma Dina Nur; Susanti, Dewi Sri
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.9814

Abstract

Inflation is a phenomenon that shows a continuous increase in the price of goods, which can cause a decline in the economic condition of a country. One of the indicators used to measure the inflation rate is the Consumer Price Index (CPI). By knowing the CPI value earlier, food prices can be controlled to be more stable. One method that can be used to predict CPI is Support Vector Regression (SVR), where this method is able to overcome linear and non-linear data conditions. This research aims to get the best prediction for CPI in South Kalimantan Province using CPI data for food groups in Tanjung, Banjarmasin, and Kotabaru in the 2014-2022 range. The best prediction results are obtained through the SVR method with Linear Kernel. The prediction error value measured through the MAPE value for Tanjung, Banjarmasin and Kotabaru is 0.77%,  and . While the size of the meaning of the model measured through the coefficient of determination, respectively 0.8826,  and . Based on these values, it is concluded that the prediction model formed is very good and feasible. The prediction results for the next 12 months show an increase, so that the government and related parties can formulate policies such as market operations and subsidy programs for the community.
ANALISIS SENSITIVITAS MODEL EPIDEMI SIR DAN SVIR PADA PENYAKIT MENULAR Munaira, Hanna; Yulida, Yuni; Karim, Muhammad Ahsar
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.12139

Abstract

Penyakit menular merupakan penyakit yang disebabkan oleh mikroorganisme patogen seperti bakteri, virus, parasit, atau jamur. Penyakit ini dapat menyebar, baik secara langsung maupun tidak, dari satu individu ke individu lainnya. Penyebaran penyakit menular dapat dimodelkan dengan pemodelan matematika epidemi Kermack-McKendrick. Penelitian ini bertujuan untuk menjelaskan pembentukan model matematika, menentukan titik ekuilibrium serta bilangan reproduksi dasar, dan menganalisis kestabilan lokal pada model matematika. Selain itu, dilakukan analisis sensitivitas terhadap bilangan reproduksi dasar dan simulasi numerik dengan metode Runge-Kutta orde 4. Dari penelitian ini, diperoleh bentuk model epidemi SIR (Susceptible, Infected, Recovered) dan modifikasi model tersebut menjadi model SVIR (Susceptible, Vaccinated, Infected, Recovered). Berdasarkan model yang terbentuk, diperoleh titik ekuilibrium bebas penyakit dan titik ekuilibrium endemik pada masing-masing model. Bilangan reproduksi dasar masing-masing model ditentukan dengan menggunakan metode Next Generation Matrix. Kemudian, dengan menggunakan nilai eigen dari matriks Jacobian, diketahui jenis kestabilan kedua model pada masing-masing titik ekuilibrium adalah stabil asimtotik lokal dengan syarat tertentu. Analisis sensitivitas menunjukkan parameter yang paling sensitif terhadap perubahan bilangan reproduksi dasar jika diurutkan dari yang terbesar untuk model SIR adalah laju penularan, laju kelahiran/kematian, dan laju kesembuhan. Sedangkan, untuk model SVIR adalah laju penularan, laju kelahiran/kematian, laju kesembuhan, dan proporsi populasi yang telah divaksinasi. Analisis-analisis ini juga diperkuat oleh hasil simulasi numerik.
CUBIC SPLINE INTERPOLATION TO APPROXIMATE SEA DEPTH BETWEEN TELUK SUAK AND LEMUKUTAN ISLAND Hariski, Muhammad; Kusumastuti, Nilamsari; Yudhi, Yudhi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.10813

Abstract

Interpolation is a technique that determines the value of a function at a point located between several known data points. Various interpolation methods include polynomial interpolation, Lagrange interpolation, Newton interpolation, and spline interpolation. Cubic spline interpolation aims to produce accurate approximations characterized by minimal oscillations in the resulting curve. This research uses the cubic spline interpolation method to estimate the sea depth in the waters between Teluk Suak and Pulau Lemukutan. The sea depth measurements are conducted to acquire information regarding the underwater topography. We collected data points using remote sensing techniques through Google Earth Pro. These points are selected based on the sea depth profile considerations, including steep areas and points of depth variation to maintain the seabed conditions within the interpolation curve, with a total of 31 data points. Subsequently, we subjected these data points to the conditions necessary for cubic spline interpolation, resulting in a system of 120 linear equations. After solving this system of linear equations, we obtained cubic spline interpolation polynomials for each subinterval and then estimated the sea depth at other points. Based on the cubic spline interpolation results, we achieved a Mean Average Percentage Error (MAPE) of 1.58%, indicating a highly accurate interpolation outcome.
PERBANDINGAN ESTIMASI VOLATILITAS HARGA OPSI BELI SAHAM APPLE INC. (AAPL) DENGAN METODE BISECTION DAN SECANT Radinasari, Nur Ismi; Sulistianingsih, Evy; Martha, Shantika
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 1 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i1.11638

Abstract

Stock price volatility is a measure of how far a stock price moves in a given Stock price volatility is a measure of how far a stock price moves in a given time. The theory developed by Black-Scholes states that every option price with the same 'underlying asset' and the same time to maturity but with different exercise values will have the same Implied Volatility value. However, this is not always the case in the market. Therefore, it is necessary to estimate volatility known as Implied Volatility, which is considered an appropriate method in estimating volatility values. This study compares the Bisection and Secant methods to estimate the volatility of Apple Inc. (Aapl) stock. This study uses data on the closing price of the stock in the period September 29, 2022 to September 29, 2023. Volatility estimation for the Bisection and Secant methods by determining the initial approximation and limiting it to a maximum of 100 simulations and iteration stops if it has produced a relative error smaller than  = . The  is an error tolerance limit, the smaller the error tolerance, the more accurate it is. According to the research results, the Bisection method produces an estimated volatility value of 0.498212 at the 9th iteration, while the Secant method produces an estimated value of 0.498590 at the 10th iteration. The Secant method produces a smaller relative error value of 0.000096, indicating that the Secant method is more accurate than the Bisection method.

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