Jurnal Riset dan Aplikasi Matematika (JRAM)

KARAKTERISTIK RING BILANGAN BULAT P-ADIC

2024-04-15T22:18:13+07:00

A p-adic integers is a formal series of a=∑_a_iP^i where 0≤a_i≤p-1 where the set of all p-adic numbers is denoted as Z_p. One of particular property of Z_p is (Z_p,+,∙) is a commutative ring with identity element. In particular, in this research, we will prove that ring Z_p is an integral domain. Furthermore, we will investigate the form of unit element and also the form of all ideals in ring Z_p.

A COMPETITION MODEL FOR THE STUDENTS RECRUITMENT BASED ON THE GENDER

2024-04-23T14:11:54+07:00

We consider a competition model describing the predator-prey interaction. Here, the student
population is divided into two sub-populations, namely male student and female student. We assume that the competition occurs not just on the same gender, but also different gender. We perform
dynamical analysis including the existence and the local stability of equilibria. It is shown that the
model has four equilibria. Our analysis shows that the male and female students do not exist, if
the intrinsic growth rate is less than one. Furthermore, if the intrinsic growth rate is greater than
one, then the coexistence of student equilibria exists. It means that the recruitment process on the
student determines the growing effects of the student population at the school. The results show
that there has been a student recruitment for SMA Negeri 50 Maluku Tengah in Maluku Province,
Indonesia. The dynamics of the recruitment system are confirmed by the numerical simulations.

PENERAPAN VALUE-AT-RISK DAN CONDITIONAL-VALUEAT-RISK DALAM PENGUKURAN RISIKO PORTOFOLIO OPTIMAL MENGGUNAKAN PENDEKATAN SIMULASI MONTE CARLO

2024-04-21T15:50:20+07:00

Saham merupakan salah satu jenis investasi yang banyak diminati karena memiliki potensi memberikan keuntungan yang tinggi dibandingkan dengan instrumen keuangan lainnya. Namun, seiring dengan potensi keuntungan yang tinggi, saham juga memiliki tingkat risiko yang sejalan dengan keuntungannya. Untuk meminimumkan risiko tersebut, pembentukan portofolio optimal menjadi salah satu strategi yang dapat dilakukan. Penelitian ini bertujuan untuk mengukur nilai risiko dari portofolio optimal dengan menerapkan metode Value at Risk (VaR) dan Conditional Value at Risk (CVaR) menggunakan pendekatan simulasi Monte Carlo. Pembentukan portofolio optimal dilakukan menggunakan single index model untuk memilih saham-saham potensial yang akan dimasukkan dalam portofolio. Berdasarkan hasil analisis dari 29 saham yang konsisten masuk indeks LQ45 periode 01 oktober 2021 hingga 01 oktober 2023, diperoleh 2 saham terpilih yakni PT. Medco Energi Internasional Tbk dan PT. Bank Mandiri (Persero) Tbk, dengan besaran proporsi dana masing-masing sebesar 76,20% dan 23,80%. Selain itu, hasil pengukuran risiko portofolio tersebut menunjukkan bahwa nilai VaR sebesar -0,04185332 dan CVaR sebesar -0,05413795. Hal ini mengindikasikan bahwa besarnya kemungkinan kerugian maksimum dari portofolio tersebut adalah 4,185332% dari modal investasi. Namun, terdapat kemungkinan lebih buruk sehingga menyebabkan investor mengalami kerugian terbesar melebihi nilai VaR yakni 5,413795% dari dana investasi dalam jangka waktu 1 hari.

Stocks are a type of investment in high demand because they have the potential to provide high returns compared to other financial instruments. However, along with high profit potential, stocks also have a level of risk that is in line with profits. Optimal portfolio formation is one of the strategies that can be implemented to minimize risk. This study aims to measure the risk value of the optimal portfolio by applying the value-at-risk (VaR) and conditional value-at-risk (CVaR) methods using the Monte Carlo simulation approach. Optimal portfolio formation is performed using a single-index model to select the potential stocks to be included in the portfolio. Based on the results of the analysis of 29 stocks consistently included in the LQ45 index for the period October 01, 2021, to October 01, 2023, two stocks were selected: PT Medco Energi International Tbk and PT Bank Mandiri (Persero) Tbk, with a proportion of funds of 76.20% and 23.80%, respectively. In addition, the results of the portfolio risk measurement show that the VaR values are -0.04185332 and -0.05413795. This indicates that the maximum possible loss of the portfolio is 4.185332% of investment funds. However, there is a worse possibility that causes investors to experience the largest loss exceeding the VaR value of 5.413795% of investment capital in a period of one day

PENGUKURAN RISIKO VAR DAN EXPECTED SHORTFALL PADA PREDIKSI HARGA MINYAK MENTAH DENGAN GEOMETRIC BROWNIAN MOTION

2024-04-21T15:48:31+07:00

Measuring the risk of crude oil commodity prices is very important for investors and policy makers, as crude oil plays an important role in economic growth. Commonly used risk measures are Value at Risk (VaR) and Expected Shortfall (ES). This study aims to calculate VaR and ES on West Texas Intermediate (WTI) crude oil commodity prices predicted using Geometric Brownian Motion (GBM). The steps taken include: calculating the predicted stock return value, conducting a normality test on the predicted stock return data, estimating parameters, calculating the VaR value using Monte Carlo simulation, and calculating the ES value. The results obtained show that the VaR value at the 90%, 95%, and 99% confidence levels is 0.02836; 0.03692; 0.05298 within the next one day and 0.06342, 0.08256, 0.11847 within the next five days. While the ES values at the 90%, 95%, and 99% confidence levels are 0.04212; 0.04937; 0.06356 in the period of one day ahead and 0.09419; 0.11039; 0.14212 in the period of five days ahead.

THE EFFECT OF OVERSAMPLING TECHNIQUES ON MACHINE LEARNING ALGORITHM IN BODY MASS INDEX (BMI) CLASSIFICATION

2024-04-27T12:58:01+07:00

BMI is the basic of people’s weight classification that can indicate serious diseases such as obesity. Many researches have been published about BMI classification using machine learning algorithms. Some techniques are used to increase the accuracy of the model, one of them is oversampling as a technique to handle imbalance data. The goal of this research is to compare the effect of either the existence and inexistence of oversampling in KNN, random forest, and SVM. The dataset that is used in this research is a real BMI classification data including gender, height, weight, and BMI index. The methods of this research are data pre-processing, data exploration, training and testing model, model’s evaluation, tuning hyperparameter, and also identify feature importance. The results of data exploration show that weight is the variable which has the strongest correlation with BMI index of 0.8 and there’s also no multicollinearity. Model’s evaluation using confusion matrix based on F1-score shows that the best model is the SVM model without oversampling after tuning hyperparameter with F1-score of more than 0.95. Feature importance’s identification using PFI methods on the best model shows that weight is the most impactful variable in BMI classification.