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All Journal EKSAKTA: Journal of Sciences and Data Analysis Media Statistika MATEMATIKA Bionatura Statistika CAUCHY: Jurnal Matematika Murni dan Aplikasi SEMIRATA 2015 Kubik JURNAL ILMU MANAJEMEN DAN BISNIS Jurnal Matematika Sains dan Teknologi Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri BAREKENG: Jurnal Ilmu Matematika dan Terapan Zero : Jurnal Sains, Matematika, dan Terapan Teorema: Teori dan Riset Matematika International Journal of Supply Chain Management Jambura Journal of Mathematics Komputasi: Jurnal Ilmiah Ilmu Komputer dan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) InPrime: Indonesian Journal Of Pure And Applied Mathematics KUBIK: Jurnal Publikasi Ilmiah Matematika International Journal of Business, Economics, and Social Development International Journal of Research in Community Services Operations Research: International Conference Series International Journal of Global Operations Research International Journal of Quantitative Research and Modeling International Journal of Ethno-Sciences and Education Research Jurnal Matematika Integratif Agridev Journal : Agribusiness Digitalization & Community Development Mathematical Sciences and Applications Journal International Journal of Technology and Education Research Indonesian Actuarial Journal
Sukono Sukono
Departemen Matematika, Fakultas MIPA, Universitas Padjadjaran
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Comparison between Holt Winter Additive and Holt Winter Multiplicative Methods in Forecasting Bank Central Asia (BBCA) Stock Price in Indonesia Stock Exchange Alem Huga Martono; Ruben Clynton Oey; Sukono
International Journal of Quantitative Research and Modeling Vol. 7 No. 1 (2026): International Journal of Quantitative Research and Modeling
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v7i1.1237

Abstract

Stock market investment plays a pivotal role in the Indonesian economy as a source of capital formation and wealth creation for investors. As a financial instrument, the performance of stock markets is determined by the ability to predict future price movements accurately to minimize investment risks and maximize returns. Bank Central Asia (BBCA) is one of the largest private banks in Indonesia and is strategically positioned as one of the most actively traded and liquid stocks in the Indonesia Stock Exchange (IDX), consistently included in the LQ45 index. This research aims to determine the proper forecasting method for the existing data patterns of BBCA stock prices and to provide more accurate forecasting results for investment decision-making. The methods used include Holt Winter Additive and Holt Winter Multiplicative exponential smoothing techniques. The dataset comprises daily closing prices of BBCA stock from December 2, 2024, to December 5, 2025, totaling 241 trading days. From these two methods, the forecasting accuracy was evaluated using Mean Absolute Percentage Error (MAPE) and Mean Squared Error (MSE). The results show that the Holt Winter Additive method has the smallest MAPE value of 0.86% (MSE: 5,043.71) compared to the Holt Winter Multiplicative method with MAPE of 1.01% (MSE: 6,789.32), indicating that the Additive model provides superior forecasting performance for BBCA stock price prediction in the observed period.
The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation Muhammad Arief Budiman; Edi Kurniadi; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (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.v11i1.41601

Abstract

The structure of a g-quasi-Frobenius Lie Algebra can be realized as a quasi-Frobenius Lie Algebra modules over a Lie Algebra g. This research discusses a special condition of the g-quasi-Frobenius Lie Algebra, namely when g acts on its self. This condition supports the construction of an inner derivation on g. The criterion investigated is the characterization of the g-quasi-Frobenius Lie Algebra in relation to the inner derivation. The result obtained is a criterion: a g-quasi-Frobenius Lie Algebra can be constructed on g itself if and only if the inner derivation is zero. Furthermore, several concrete examples are provided to test this criterion.
Numerical Solution of the Time-Fractional Black-Scholes Equation and Its Application to European Option Pricing Elza Rahma Dihna; Endang Rusyaman; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): 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.v10i2.35248

Abstract

The classical Black-Scholes model is widely used in option pricing but relies on idealized assumptions such as constant volatility and memoryless market dynamics, which limit its accuracy in capturing real-world financial behavior. To overcome these limitations, the time-fractional Black-Scholes model incorporates a fractional-order derivative—specifically the Caputo derivative—which introduces memory effects and accommodates time-varying volatility. This study focuses on numerically solving the time-fractional Black-Scholes equation using the finite difference method (FDM) and applying the results to the pricing of European call options. The model is discretized using an implicit finite difference scheme to ensure stability and accuracy over the time domain. Numerical simulations are conducted for various values of the fractional order α, illustrating that the option price is sensitive to the fractional parameter. Lower values of α tend to increase option prices, highlighting the influence of memory effects on pricing behavior. The results confirm that the finite difference method is an effective numerical tool for solving fractional partial differential equations and demonstrate that the fractional Black-Scholes model offers improved flexibility and realism in option  valuation, particularly in markets characterized by irregular volatility and non-Markovian features.
Systematic Literature Review: Optimal Stopping and Investment Optimization for Bankruptcy Risk Management in Sharia Insurance Setyo Luthfi Okta Yohandoko; Diah Chaerani; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): 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.v10i2.35523

Abstract

The increasing demand for Sharia-compliant financial services in Muslim-majority countries such as Indonesia has driven the rapid development of Sharia insurance (Takaful). Despite its growth, the Sharia insurance sector faces significant challenges in managing investment portfolios and mitigating bankruptcy risks. Addressing these challenges requires a comprehensive understanding of the existing mathematical and financial models configured according to Islamic principles. Several studies have introduced stochastic approaches to model surplus processes, investment returns, and risk probabilities in insurance operations. Among these, the Cramér–Lundberg model has been widely used to estimate surplus dynamics and bankruptcy risks, while the Vasicek model provides a stochastic framework for modeling investment returns. Quadratic programming has also been applied to optimize asset allocation under specific constraints. However, these methodologies have typically been explored in isolation, which limits their ability to provide an integrated and effective framework for simultaneous bankruptcy risk mitigation and Sharia-compliant investment optimization. This methodological gap constrains the advancement of comprehensive, practically applicable, and theoretically sound solutions that are specifically designed to address the distinctive operational characteristics of Shariainsurance. The objective of this systematic review of the literature is to synthesize and critically analyze the methods used in previous research and to explore how they can be systematically integrated to form a comprehensive risk and investment management framework for Sharia insurance. The review identifies the strengths, limitations, and potential for combining optimal stopping theory, stochastic surplus modeling, and investment optimization to support robust financial decision making. This review contributes by offering a structured research agenda for the development of integrated models that simultaneously address the complexities of bankruptcy risk and Sharia-compliant investment strategies. Furthermore, this study provides valuable information for academics and practitioners seeking to improve the financial sustainability of the Islamic Insurance industry.
Mean-Variance Portfolio Optimization with Lot Size Constraints in Energy Stocks: A Monte CarloApproach Willen Vimelia; Riaman Riaman; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): 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.v10i1.32159

Abstract

Stock investment requires portfolio optimization strategies that maximize returns and consider risks and practical constraints, such as target lot sizes. These constraints are crucial to ensuring the realistic implementation of portfolios in compliance with market regulations, particularly in Indonesia, where 1 lot equals 100 shares. However, existing research on the Mean-Variance model and Monte Carlo simulation has rarely incorporated target lot constraints, limiting the applicability of these models in real-world scenarios. To bridge this gap, this study conducts a systematic literature review (SLR) on portfolio optimization in Indonesia's energy sector stocks, focusing on the Mean-Variance model, risk aversion, Monte Carlo simulation, and target lot constraints. The PRISMA framework guides this SLR, with bibliometric analysis performed using RStudio. A rigorous selection process from Scopus and ScienceDirect databases yielded 13 relevant articles for in-depth analysis creates a more practical and effective approach to portfolio management. This advancement enables investors to achieve balanced portfolios that are both theoretically robust and feasible in practice. The study contributes significantly to optimizing investment strategies for Indonesia’s energy sector and opens avenues for further research into practical portfolio optimization methods.
Investment Portfolio Optimization of Mean-Entropic-VaR Model on the Top Ten Stocks from LQ45 in the Indonesian Capital Market Nurnisaa binti Abdullah Suhaimi; Herlina Napitupulu; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): 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.v10i1.30794

Abstract

In an investment portfolio, investors certainly choose a portfolio according to their preferences for return and risk. The problem is the allocation of investment weights in forming a portfolio, if the risk is in the form of Entropic-Value-at-Risk (EVaR). The purpose of this study is to determine the allocation of investment weights that maximize returns and minimize portfolio risk. The method used in this study is through investment portfolio optimization in the form of Mean-EVaR. The stages carried out are selecting the ten best stocks in the LQ45 index, estimating and testing the suitability of the return distribution, determining expectations, variance and covariance between stock returns, and optimizing the allocation of investment portfolio weights using the Mean-EVaR model. Based on the results of the analysis, it was obtained that the optimal portfolio weight allocation is 0.01073, 0.23284, 0.04617, 0.08052, 0.00470, 0.09021, 0.14669, 0.00427, 0.22672 and 0.15715, to be allocated successively to the stocks ACES, BBRI, EXCEL, ITMG, PTBA, ADRO, BBTN, GGRM, KLBF and AKRA. In this optimal portfolio, the average portfolio return is obtained at 0.00055 with an EVaR risk of 0.01632. It is hoped that the results of this study can provide a significant contribution to investors in making investments, especially in the ten stocks analyzed.
Optimization Modeling of Investment Portfolios Using The Mean-VaR Method with Target Return and ARIMA-GARCH Arla Aglia Yasmin; Riaman Riaman; Sukono Sukono
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): 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.v10i1.30042

Abstract

This research develops a portfolio optimization model using the Mean-Value at Risk (Mean-VaR) approach with a target return constraint, addressing the gap in models that specific return objectives. The ARIMA-GARCH model is utilized to predict stock returns and volatility, offering precise inputs for optimization. By applying the Lagrange method and Kuhn-Tucker conditions, the model determines optimal portfolio weights that balance risk and return. Using data from infrastructure stocks on the Indonesia Stock Exchange (January 2019-September 2024), the model’s effectiveness is validated through numerical simulations. The results illustrate efficient frontiers for target returns of 5x10^-6, 0.001, and 0.0019, revealing that higher return targets proportionally increase risk. ARIMA-GACRH’s advantage lies in its ability to capture both mean and variance dynamics, ensuring reliable volatility estimates for informed decision-making. This study contributes to portfolio optimization literature by emphasizing target return constraints and demonstrating the practical utility of volatility modeling. The findings provide a robust framework for investors to align portfolios with financial goals and risk tolerance. Future work could explore broader market contexts or integrated additional constraints for enhanced applicability.
Co-Authors Abdul Talib Bon Abiodun Ezekiel Owoyemi Achmad Bachrudin Adhitya Ronnie Effendie, Adhitya Ronnie Agung Prabowo Agung Prabowo Agung Prabowo Agus Santoso Agus Santoso Agus Sugandha Agustini Tripena Br Surbakti Aisyah Nurul Aini Alem Huga Martono Amalia, Hana Safrina Amitarwati, Diah Paramita Anastasia Audrey Wijaya Apipah Jahira, Juwita Arla Aglia Yasmin Arla Aglia Yasmin Asep K Supriatna Asep Saepulrohman Asep Solih Awalluddin, Asep Solih Asri Rula Hanifah Aulia Kirana Aulya Putri Ayyinah Nur Bayyinah Aziza Ayu Nurjannah Azizah Rini Widyani Bakti Siregar Banowati, Puspa Dwi Ayu Basuki , Basuki Basuki Bayyinah, Ayyinah Nur Betty Subartini Betty Subartini Betty Subartini Bimasota Aji Pamungkas bin Mamat, Mustafa Budi Pratikno Candra Budi Wijaya Carissa, Katherine Liora Dara Selvi Mariani Dedy Rosadi Dedy Rosadi DEWI RATNASARI Dhika Surya Pangestu Diah Chaerani Diah Paramita Amitarwati Diana Ekanurnia Dini Aulia Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Eddy Djauhari Edi Kurniadi Edi Kurniadi Elza Rahma Dihna Ema Carnia Emah Suryamah, Emah Eman Lesmana Endang Rusyaman Endang Soeryana Hasbullah Estu Putri Dianti Fadia Irsya Septiana Fasa, Rayyan Al Muddatstsir Febrianty, Popy Firdaus, Muhammad Rayhan Forman Ivana S. S. S. Gani Gunawan Ghazali, Puspa Liza Grida Saktian Laksito Hadiana, Asep Id Hana Safrina Amalia Haq, Fadiah Hasna Nadiatul Hasbullah, Soeryana Hasriati Hasriati Hazelino Rafi Pradaswara Herlina Napitupulu Hidayana, Rizki Apriva Himda Anataya Nurdyah Ibrahim M Sulaiman Ihda Hasbiyati Iin Irianingsih Ira Sumiati Ismail Bin Mohd Januaviani, Trisha Magdalena Adelheid Jehan Rizky Faustina Hartono Jessica Novia Sitepu Jessica Sie Jumadil Saputra Jumadil Saputra Kahar, Ramadhina Hardiva kalfin Kalfin Kalfin, Kalfin Katherine Liora Carissa Khairi, M. Ihsan Kirana Fara Labitta Labitta, Kirana Fara Linda Damayanti Putri Lutfi Praditia Ma’mur M. Ihsan Khairi Maraya, Nisrina Salsabila Maudy Afifah Audina Maulana Malik Maulida, Ghafira Nur Ma’mur, Lutfi Praditia Melina Melina Mochamad Suyudi Mohamad Nurdin, Dadang Muhammad Arief Budiman Muhammad Arief Budiman Muhammad Iqbal Al-Banna Ismail Mustafa Mamat Mustafa Mamat Mustafa Mamat Mustafa Mamat Mustafa Mamat Nabilla, Ulya Nadia Putri Riadi Nahda Nabiilah Naia Rafida Mumtaz Nisrina Salsabila Maraya Nita Rulianah Noriszura Ismail Norizan Mohamed Novianti, Saqila Novieyanti, Lienda Novinta S, Fujika Novitasari, Ela Nugraha, Dwita Safira Nur Mahmudah Nurdyah, Himda Anataya Nurfadhlina Abdul Halim Nurnisaa binti Abdullah Suhaimi Nurul Fadilah Pardede, Ester Popy Febrianty Priyatna, Yayat Puspa Liza Ghazali Putri, Aulya Putri, Linda Damayanti Putri, Sherina Anugerah Raharjanti, Amalia Rahman, Rezki Aulia Ramdhania, Tya Shafa Ratih Kusumadewi Rayyan Al Muddatstsir Fasa Riadi, Nadia Putri Riaman Riaman Riaman Riaman Rini Cahyandari Riza Adrian Ibrahim Rosadi, D. - Ruben Clynton Oey Rulianah, Nita Saefullah, Rifki Salamiah, Mia Salih, Yasir Sampath, Sivaperumal Saputra, Jumadil Setyo Luthfi Okta Yohandoko Shindi Adha Gusliana Sianturi, Sri Novi Elizabeth Sisilia Sylviani Siti Sabariah Abas Soeryana Hasbullah Sri Novi Elizabeth Sianturi Sri Purwani Stanley Pandu Dewanto Subanar - Subanar . Subanar Subanar Subiyanto Subiyanto Sudradjat Supian Sulastri, S Sumiati, Ira Supian, Sudradjat Supriyanto Supriyanto Suroto Suroto Susanto, Sunarta Sutiono Mahdi Sutisna, Sarah Suyudi, Mochamad Suyudi, Mochammad T.P Nababan Tampubolon, Carlos Naek Tua Tika Fauzia Titi Purwandari Titin Herawati Umar A Omesa Valentina Adimurti Kusumaningtyas Verrany, Maria Jatu Wan Muhamad Amir W Ahmad Widyani, Azizah Rini Wiliya Wiliya Willen Vimelia Willen Vimelia Yasir Salih Yhenis Apriliana Yulianus Brahmantyo Yulison Herry Chrisnanto Yuningsih, Siti Hadiaty Yuyun Hidayat Zahra, Ami Emelia Putri Zinedine Amalia Noor Mauludy Reihan