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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 579 Documents
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Marine Insurance: Frequency–Severity Claim Modeling and the Effect of Delay on Ruin Probability Sandy Salomo Saruan; Adhitya Ronnie Effendie; Rana Sahilah
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.v11i2.44875

Abstract

Reporting dates do not identify claim payment times. We quantify a reporting-based payment-time assumption's effect on finite-horizon cash ruin in an idealized marine portfolio. The freMarine calibration comprises 1,109 positive-payment snapshot claims over 41 occurrence months, with negative-binomial monthly counts, finite-mixture severity, and empirical zero-inflated reporting lags. Refitted-bootstrap diagnostics assess distributional adequacy; conflicting severity diagnostics and rejected parametric lag fits remain explicit. Event-driven simulation couples immediate and proxy payments on the same occurrences and severities, with constant aggregate premiums and an empty initial system. For 250,000 paired paths over 60 months at initial surplus 2,000 EUR thousands, cash-ruin estimates are 0.2951/0.2363 for immediate/proxy payment. The paired difference is -0.0588 (95% conditional Monte Carlo interval [-0.0597,-0.0579]); mean outstanding payments are 718.79 EUR thousands. Nonnegative delay mechanically favors coupled cash surplus without discharging liabilities. Unobserved payment histories, opening claims, and policyholder behavior preclude claims of predictive superiority, a preferred handling policy, or regulatory capital needs.
Copula Regression for Deductible--Claim Dependence in Non-Life Insurance: A Stratified Evaluation Dwi Mifta Mahanani; Feby Indriana Yusuf; Dzaki Ferlian Nugroho; Tuti Sariningsih Budi Utami
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.v11i2.43524

Abstract

Deductible choice may be statistically associated with claim outcomes after observed rating variables have been taken into account. The contractual deductible is distinguished from the normalized deductible ratio used as the continuous working margin, while claim count remains discrete and individual severity remains continuous. A Canonical Vine pair-copula construction links the deductible ratio, claim frequency, and individual claim severity. The application uses 1,038 entities from the Wisconsin Local Government Property Insurance Fund observed from 2006 to 2010; models are estimated on 2006-2009 data and evaluated on the 2010 temporal holdout. The estimated dependence is negative for deductible-frequency, positive for deductible observed severity, and negative for frequency-severity conditional on the deductible. These patterns are interpreted as conditional associations that may be consistent with selection and claim-reporting mechanisms, rather than as causal evidence of adverse selection or moral hazard. The dependence model attains a higher observation-level logarithmic score than the exogenous-deductible benchmark for 64.55% of frequency observations and 71.09% of severity observations. Its global Insurance Gini  improvement is 22.54 points, with positive point estimates across all five deductible strata but greater uncertainty in the highest-deductible group. The results show that deductible information can improve out of sample risk discrimination, while also demonstrating the importance of support assumptions, benchmark definitions, and cautious behavioral interpretation.
Sobol and GJR-GARCH for Dominant Factors of European Option Prices in Blue-Chip Index Constituent Stocks Nathania Azzah Mu’azara; 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.v11i2.45307

Abstract

Conditional volatility-based option pricing research generally emphasizes improving volatility inputs, but has not yet fully explained the relative contribution of each parameter to variation in simulated option-pricing responses for Indonesian index stocks. This study integrates BlackScholes, GJR-GARCH asymmetric volatility, and Sobol global sensitivity analysis to identify dominant factors in a model-generated European call-option response for verified constituents of an Indonesian blue-chip index, denoted Index X. The sample consists of 19 constituents that remained consistent from February 2022 to December 2025. Logarithmic returns are tested for stationarity and ARCH effects, conditional volatility is estimated using GJR-GARCH(1,1), and the BlackScholes response is evaluated with five independently and uniformly distributed inputs: moneyness, maturity, risk-free rate, volatility multiplier, and proportional transaction cost. The results show that all returns are stationary and most stocks exhibit significant ARCH effects. Under the baseline domain, maturity and moneyness are the leading factors, while the volatility multiplier is secondary and the risk-free rate and transaction cost have smaller contributions. The ranking remains contract-dominated under a wider scenario domain and under a Student-t innovation check, although the magnitudes and ordering of maturity and moneyness can change. The contribution of this research is sensitivity decomposition of a specified BlackScholes response with a GJR-GARCH-based volatility input, not evidence of improved pricing accuracy against observed option prices. Issuer and index identities are masked in the manuscript to prevent issuer-specific model outputs from being misconstrued as investment recommendations or comparative assessments; a confidential identity crosswalk is retained for editorial verification.
Randomness Test of LightMAC-Based Pseudorandom Number Generator (PRNG) with NIST SP 800-22 Revision 1A Test Bety Hayat Susanti; Wahyu Achmad Fadiel; Yeni Farida; Obrina Briliyant
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.v11i2.43424

Abstract

Random numbers are essential for ensuring the security and unpredictability of cryptographic systems; however, resource-constrained devices still lack effective lightweight random number generators. This gap leaves encryption, authentication, and key generation vulnerable, exposing critical infrastructure to adversarial exploitation. This study presents the development and statistical evaluation of a Pseudo-Random Number Generator (PRNG) based on the LightMAC construction instantiated with the PRESENT lightweight block cipher. The proposed PRNG operates by iteratively processing a fixed seed message through LightMAC-PRESENT with a varying counter. The randomness of the generated bit sequences was rigorously analyzed using the NIST SP 800-22 Revision 1A test suite. The evaluation encompassed multiple implementation configurations, including two seed message lengths ($|x|$) of 64 bits and 128 bits, two key lengths for the underlying PRESENT cipher of 80 bits and 128 bits, and three counter lengths of 8 bits, 16 bits, and 32 bits. The results demonstrate that the LightMAC-PRESENT-based PRNG satisfies the NIST statistical requirements under specific parameter configurations. For a 64-bit seed message, a 128-bit PRESENT key combined with an 8-bit or 16-bit counter successfully passes all tests. For a 128-bit seed message, the generator achieves compliance with an 80-bit key and a 128-bit key. The optimal configuration identified is a 128-bit seed message, an 80-bit key, and a 16-bit counter, which passes all tests across all key-pattern variations. These findings provide critical insights into the optimal parameters for secure, efficient, lightweight deterministic random bit generation in resource-constrained environments.
Classification of Educational Vulnerability Status Using Boosting Methods on Imbalanced Socioeconomic Data Andi Illa Erviani Nensi; Meavi Cintani; Mahda Al Maida; A. Qeis Tenridapi; Bagus Sartono; Aulia Rizki Firdawanti; Budi Susetyo; Gerry Alfa Dito
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.v11i2.39670

Abstract

Extreme class imbalance in educational data causes classification models to favor the majority class and fail to identify vulnerable students who are not attending school, despite this group requiring the greatest intervention. This study aims to develop a classification model for identifying educational vulnerability status among school-age children. The positive class corresponds to out-of-school children (minority class), while the negative class represents children who are still attending school. The dataset exhibits an extreme imbalance ratio of approximately 1:48, making conventional classification approaches ineffective in detecting minority-class observations.To address this challenge, four imbalance-aware boosting methods, namely AdaBoost-M2, SMOTEBoost, RBBoost, and RUSBoost, were compared. Model selection was conducted using stratified five-fold cross-validation on the training set, followed by final evaluation on an independent test set. Model performance was assessed using sensitivity, specificity, balanced accuracy, and Area Under the Curve (AUC), which are more appropriate than overall accuracy for highly imbalanced data. The results show that SMOTEBoost L50 with a threshold of 0.50 achieved the highest Balanced Accuracy (0.7474), Sensitivity (0.8824), and AUC (0.7745). However, its low minority-class precision (0.0452) and F1-score (0.0860) indicate a substantial false-positive trade-off. These findings demonstrate that integrating minority-class balancing strategies with boosting mechanisms can substantially improve the detection of vulnerable students in highly imbalanced socioeconomic data. Feature importance analysis revealed that education level or class was the most dominant predictor, followed by household size and frequency of internet use. Overall, this study provides empirical evidence regarding the effectiveness of imbalance-aware boosting methods for educational vulnerability detection and highlights their potential application in supporting more targeted educational interventions.
Modified Black-Scholes Model for Valuing Employee Stock Options with Constant Exit Rate: A Case Study of a Banking Company in Indonesia Permadi Yulianto; 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.v11i2.45561

Abstract

Employee Stock Options (ESO) are a form of compensation given to employees in the form of shares that can be purchased within a specified period. The ESO valuation uses the Black Scholes model, assuming employees remain employed until the vesting period is completed, excluding the employee’s departure from the company before the option rights are exercised. This study aims to determine the value of Employee Stock Options (ESO) by adding a constant exit rate factor. The data from this study are the closing price at BANK XYZ for the calculation of Volatility, for the risk-free interest rate from the Federal Reserve Bank of St. Louis used to calculate the option value using the Black-Scholes model, adjusted for the probability of continued employment (survival probability) obtained from various constant exit rate values. The results of the study using the constant exit rate produce a lower Employee Stock Option value than the calculation using the standard Black-Scholes model. The decline is greater with increasing maturity time because the employee’s probability of remaining employed at the company decreases. By applying a constant exit rate, the assessment results better reflect the real conditions compared to the Black-Scholes model, which does not consider the risk of employee departure from the company
Determining Logistics Route Capacity Using Maximal Solutions of Two-Sided Max-Min Linear System with Python Implementation Zakia Nur Ramadhani Putri; Ari Suparwanto; Sutopo Sutopo
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.v11i2.44534

Abstract

Max-min algebra, equipped with maximum and minimum operations, provides a natural framework for modeling systems with bottleneck constraints, such as logistics and transportation networks. An algorithm for solving two-sided linear systems of the form A x = B x in max-min algebra has been proposed, for which the maximal solution can be constructed explicitly for the 1 n case under three conditionsunconstrained, with a given upper bound, and with a given lower boundand generalized to the m n case, terminating after at most m iterations and producing a unique maximal solution with complexity O(m2n). However, no implementation has been made available, which limits its use for larger, practically sized problems: the algorithm may require up to m computational cycles, so the computational burden grows with the matrix sizeparticularly the number of rowsand manual calculation becomes more prone to error. This paper addresses this gap by providing a Python implementation of the algorithm, along with a numerical application to a logistics distribution network. The Python implementation makes the algorithm accessible to practitioners, and the logistics example demonstrates how the model can be used to determine optimal road capacities. This work provides a practical computational tool for solving capacity planning problems in logistics and transportation.
Packing Chromatic Number of Graph Families Constructed from the Fan Graph Raventino Raventino; Fransiskus Fran; Yudhi Yudhi
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.v11i2.44807

Abstract

Packing coloring is particularly sensitive to graph distances, since even a simple structural modification may change whether a color can be reused. This paper investigates the packing chromatic number of several constructions derived from the fan graph, namely the subdivision fan S(Fn), the umbrella graph Ur,s, two barbell-type fan constructions, and the generalized q-fan chain CFm(q) formed by sequentially joining the centers of q copies of Fm. The known packing chromatic number of the ordinary fan is used only as a reference result. By combining explicit packing colorings with lower bound arguments based on independence numbers, graph diameters, color class capacities, and cross-component distances, we prove that (S(Fn)) = 4 for n 2 and determine the exact packing chromatic numbers of the umbrella and both barbell-type constructions. For CFm(q), we establish general lower and upper bounds for all m, q 2 by showing that a color 2 can occur on at most q/( 1) vertices. Moreover, when m 2q 2, the bounds coincide and yield (CFm(q)) = q(m/2 + 2) t=1q1q/t. These results show that the packing chromatic behavior of fan-derived graphs is governed by the distance structure created by the underlying graph operation, particularly the extent to which low colors can be reused across different fan copies.
Climate Risk in ESG Portfolios: Evidence from Indonesian Equity Markets Annisa Syalsabila; Nur Ikhwana; Lalu Ramzy Rahmanda
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.v11i2.45016

Abstract

We examine climate variables in a pipeline for dynamic Value-at-Risk (VaR) of the SRI-KEHATI ESG index and the IHSG (Jakarta Composite Index). Using 1,499 daily observations (20142025), we combine the Least Absolute Shrinkage and Selection Operator (LASSO) over 50 candidate predictors, a quantile regression neural network (QRNN) for VaR at three quantile levels, and SHAP for attribution. LASSO removes all climate variables from both indices. For IHSG, the partial correlation of clean-energy returns falls from 0.121 to 0.0005 once domestic equity factors enter, consistent with domestic absorption, though constituent overlap cannot exclude a purely compositional explanation. A diagnostic quantile regression shows climate contributions rising 2.82-fold from VaR 90% to VaR 99%, but the pattern is flat under the QRNN itself (ratio 1.03). In the main backtest, QRNN has lower pinball loss than Historical Simulation and GARCH(1,1)-t in all 12 DieboldMariano comparisons (p 0.001), although it uses same-day predictors the benchmarks lack and the advantage was not reproduced in the ablation. In a common-sample ablation (n = 249 of 300 nominal test days), LASSO pre-selection is associated with 4 of 6 Kupiec passes versus 0 of 6 without it, but IHSG still fails at two of three quantile levels. Whether SRI-KEHATI screening isolates climate risk was not tested; mediation covers IHSG only.
Comparative Evaluation of Hyperparameter Optimization Strategies for k-Nearest Neighbors over Mixed Domain Search Spaces Meta Kallista; Ig. Prasetya Dwi Wibawa; Heni Widayani
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.v11i2.42295

Abstract

k-Nearest Neighbors (KNN) remains a strong baseline due to its simplicity, interpretability, and non-parametric structure; however, its predictive performance is highly sensitive to interacting hyperparameters. This paper studies search-constrained hyperparameter optimization for KNN over a mixed search space comprising an integer neighborhood size, a categorical distance metric, and a continuous Minkowski exponent. Seven tuning strategies are compared under a unified nested validation protocol with standardized preprocessing: grid search, random search, Bayesian optimization, genetic algorithm, surrogate optimization, particle swarm optimization, and grey wolf optimizer. Experiments on diverse public classification datasets from UCI, OpenML, and Kaggle evaluate predictive performance (accuracy, macro-AUC, cross-entropy), validation loss, and runtime. The results indicate that adaptive optimizers generally provide more favorable performancecost trade-offs than exhaustive grids under limited evaluations, while no single method is uniformly best across all datasets. Rank-based statistical comparisons using non-parametric tests further support the observed differences and motivate practical recommendations for selecting tuning strategies as a function of evaluation search and mixed-domain search-space characteristics.

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