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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 548 Documents
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Remodeling and Application of Stock Option Price Based on Skewed Laplace Distribution Approach Evy Sulistianingsih; Ferdi Afrizal; Muhammad Fikri; Pitriani -
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44222

Abstract

This paper proposed a new model to price a stock option based on the Skewed Laplace distribution approach (SLOP). The approach was considered to provide a better option price than Black Scholes Option Price (BSOP) because Skewed Laplace distribution (SL) has a shape parameter that can capture excess skewness and kurtosis frequently found in stock return underlying the option price. In this study, SL’s shape parameter was estimated using a mixture of the Moment Method and Fourth-Order Taylor Series approach. The estimator was different from the majority of prior SL’s shape parameter that was obtained by Maximum Likelihood Estimation (MLE). The proposed shape parameter was easier to obtain relative to the prior parameter because it did not require a Likelihood Function (LH) and the maximization of LH where involved a complicated numerical method. The performance of SLOP was applied to eleven different enterprises that trade stock options at several strike prices. According to the empirical results in this research, it can be summarized that the SL approach yields a better option price model rather than Black Scholes (BS).
Consensus Bayesian Network Learning for Market Basket Analysis in Indonesian Retail Transactions Muhammad Sahid; I Gede Mindra Jaya; Restu Arisanti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.41879

Abstract

Understanding relationships among products in retail transactions is essential for supporting strategic decisions such as product placement and cross-selling. However, traditional market basket analysis is limited to pairwise associations and cannot capture complex conditional dependencies among multiple items. This study addresses these limitations by applying a Bayesian Network framework to model product relationships probabilistically. Transaction data collected over one month were transformed into a binary dataset of 441 transactions across 31 product categories. The network structure was learned using a stochastic search algorithm with a Bayesian Dirichlet equivalent (BDe) score, enhanced by a multi-seed strategy and edge support aggregation to ensure robustness. Parameters were estimated using maximum likelihood. The results indicate that relationships are both directional and context-dependent, with snack probabilities increasing with instant noodles but decreasing when cigarettes are also present. The LOIO accuracy is 0.6659.
Modified Multigroup Ramsey RESET for Specification Detection in Semiparametric Path Models M. Dziqri nur Rohiim; Adji Achmad Rinaldo Fernandes; Achmad Efendi; Mujiono Mujiono; Kamelia Hidayat
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43782

Abstract

This study develops a modified multigroup Ramsey RESET (Regression Equation Specification Error Test) within a semiparametric multigroup path model, a statistical framework that combines parametric and nonparametric approaches across multiple groups. Developed using dummy-variable interactions, the method identifies both linear and truncated spline relationships and enables analysis of all groups within a single integrated model, eliminating the need for separate group tests. Simulation studies using empirical data on students’ AI literacy applied combinations of linear and truncated-spline relationship patterns. The method was evaluated using the p-value, Correct-to-Incorrect p-value Ratio, Dominance Ratio, and Accuracy. The results indicate that the modified multigroup Ramsey RESET generally produces larger p-values for models that match the underlying data-generating mechanism than for competing alternative models, demonstrating good discriminatory power in identifying appropriate model specifications. The empirical application further reveals that several relationships among variables exhibit truncated spline patterns rather than purely linear forms. Thus, the proposed method provides an alternative specification test for simultaneously identifying linear and nonlinear relationships within multigroup semiparametric path models.
Spatio-Temporal Forecasting and Continuous Spatial Reconstruction of Fire Radiative Power Using Sequential GSTARX-IDW and Ordinary Kriging Nurfitri Imro'ah; Nur'ainul Miftahul Huda; Yundari Yundari; Gita Fitriyana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44480

Abstract

This study presents a sequential hybrid spatio-temporal forecasting framework combining the Generalized Space-Time Autoregressive with Exogenous Variables (GSTARX-IDW) model and Ordinary Kriging (OK) to model and map weekly Fire Radiative Power (FRP) dynamics in West Kalimantan from January 2021 to October 2025. A strong dominance of spatial contagion was observed, with the spatial autoregressive parameter (p1) being statistically significant across 95.56% of operational grid centroids, providing empirical validation of Tobler's First Law of Geography. Locally, Land Surface Temperature (LST) serves as a key exogenous forcing variable, exhibiting geographical dichotomies driven by localized microclimatic conditions and peatland hydrology. To overcome the limitation of discrete point forecasts at grid centroids, Ordinary Kriging was applied directly to the k-step ahead GSTARX-IDW point forecasts, successfully reconstructing continuous spatial risk surfaces for October 2025. Evaluated through robust out-of-sample metrics, the framework achieved a Root Mean Squared Error (RMSE) of 1.1380, a Mean Absolute Error (MAE) of 0.8736, and a Mean Absolute Scaled Error (MASE) of 1.0008, demonstrating competitive temporal point forecasting on par with baseline dynamics while offering superior spatial continuous risk mapping. This sequential framework provides a mathematically grounded baseline for short-term spatio-temporal risk assessment in highly fragmented tropical landscapes.
Bankruptcy Risk Analysis and Estimation of Healthy and Distressed Stocks Using Extended Black-Scholes Model Ram Daniel Andrian Vernando; Rudianto Artiono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44791

Abstract

The classical Black-Scholes model assumes that stock prices follow a Geometric Brownian Motion (GBM) process, in which stock prices remain strictly positive throughout time. However, this assumption restricts the model’s capability to represent firms experiencing financial distress, where stock prices may gradually approach zero as bankruptcy risk increases. This study employs the Extended Black-Scholes Model (EBSM), which introduces a stoppingtime mechanism that enables stock prices to reach the bankruptcy boundary, to analyze and compare bankruptcy risk characteristics between financially healthy and distressed stocks. Historical adjusted closing price data from Microsoft Corporation (MSFT.US) and Bed Bath Beyond Inc. (BBBY.US) were utilized, with model parameters estimated using quadratic variation and Maximum Likelihood Estimation (MLE) methods. The estimation results revealed different stochastic characteristics between the two stocks, where MSFT.US generated a positive drift parameter of 0.216682, whereas BBBY.US generated a negative drift parameter of −0.248385 along with higher volatility. The bankruptcy risk analysis demonstrated that MSFT.US produced infinite Expected Bankruptcy Time (EBT) and Conditional Expected Bankruptcy Time (CEBT) values, while BBBY.US yielded a finite EBT of 5.113633 years, with CEBT values updated according to the observed stock price conditions. These results suggest that the EBSM framework can effectively differentiate bankruptcy risk characteristics by combining stochastic stock price dynamics with time-to-bankruptcy measures.
Spatiotemporal Dynamics in Predator–Prey Models Incorporating Time Delay and Harvesting Dede Alif Permana; Diny Zulkarnaen; Dian Nuraiman
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44741

Abstract

A three-compartment predator-prey model (prey, middle predator, top predator) is developed by integrating spatial diffusion, discrete time delays (gestation and biomass conversion), and proportional harvesting on the two lower trophic levels. The objectives are to formulate the model, analyze local stability dynamics and Hopf bifurcation due to time delay variations, and determine a sustainable harvesting strategy based on the Maximum Sustainable Yield (MSY) concept. Methods include equilibrium analysis, linearization using a variation matrix, Routh–Hurwitz criterion, and numerical simulations with GNU Octave in one- and two-dimensional spatial domains. The results show that a positive interior coexistence equilibrium exists and is locally asymptotically stable under certain conditions. Single or double time delays without harvesting trigger Hopf bifurcation when exceeding critical values, while pure diffusion does not produce instability on its own. Harvesting at safe rates increases the critical delay values and maintains coexistence, in contrast to the mathematical MSY harvesting that leads to species extinction. In conclusion, the integration of diffusion, time delays, and harvesting yields complex dynamics, with time delays as the main destabilizer and controlled harvesting as a stabilizing agent that delays the onset of Hopf bifurcation.
Delay Tolerance Thresholds and Natural Recovery in a Fork-Join Production System over Max-Plus Algebra Dewa Putu Wiadnyana Putra; Marcellinus Andy Rudhito
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45031

Abstract

This study investigates server-specific delay tolerance and natural recovery in a three-server fork--join production system modeled with max-plus algebra. The system has two parallel servers synchronized by a join server and is analyzed in the canonical regime where the second-server self-loop is the unique critical circuit. Using max-plus spectral theory, critical-circuit margins, relative-delay recurrences, and computational validation, we examine a single additive event-time delay introduced after the nominal trajectory has entered the eigenvector regime. Every positive delay at the critical server propagates permanently, so its tolerance threshold is zero. At the two non-critical servers, exact finite thresholds are determined by the available margins between the critical circuit and competing non-critical paths. Delays not exceeding these thresholds are naturally absorbed without switching or control intervention, and a finite upper bound on the recovery time is established from a two-cycle contraction argument. Numerical tests across three admissible parameter sets confirm below-threshold recovery, boundary recovery, above-threshold propagation, and invariance with respect to the delay cycle and eigenvector translation. These results provide a precise event-level robustness characterization for the stated canonical fork--join regime.
A Comparative Study of Univariate and Bivariate Logistic Regression on Hypertension and Obesity Muhamad Lazuardi; A'yunin Sofro
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.43020

Abstract

Hypertension and obesity frequently co-occur and share common pathophysiological mechanisms. However, most existing studies model these conditions independently using separate logistic regression models, which ignore their dependency structure and may yield inefficient estimates. This study compares univariate and bivariate binary logistic regression approaches in modelling hypertension and obesity simultaneously, using individual-level data from the Indonesian Family Life Survey wave 5 (IFLS5), comprising 8,100 respondents. Age, sex, waist circumference, handgrip strength, lung capacity, and pulse rate were included as predictors. The bivariate model estimated a significant dependence parameter of θ = 1.216 (p = 0.010), confirming positive co-occurrence between the two conditions. Waist circumference emerged as the dominant predictor for both outcomes. Model comparison based on AIC demonstrated that the bivariate approach outperformed the combined univariate models, indicating superior fit when accounting for the dependence structure.

Page 55 of 55 | Total Record : 548

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