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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JTAM (Jurnal Teori dan Aplikasi Matematika) Zero : Jurnal Sains, Matematika, dan Terapan Teorema: Teori dan Riset Matematika Jurnal Cendekia : Jurnal Pendidikan Matematika International Journal of Supply Chain Management FIBONACCI: Jurnal Pendidikan Matematika dan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 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 Euclid Jurnal Matematika Integratif In Search (Informatic, Science, Entrepreneur, Applied Art, Research, Humanism)
Riaman Riaman
Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Padjadjaran
Religion Agriculture, Biological Sciences & Forestry Arts Humanities Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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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 AGUS SUPRIATNA Aldino Reisnanda Alim Jaizul Wahid Alit Kartiwa Anang Muhajirin Andhita Zahira Adib Annisa Aprillia Ariyanti, Devi Arla Aglia Yasmin Arla Aglia Yasmin Ary Robayani Asthie Zaskia Maharani Atha Hukama Aulianda Anisa Putri S. R. Aulya Putri Ayyinah Nur Bayyinah Azizah Rini Widyani Bayyinah, Ayyinah Nur Betty Subartini Betty Subartini Betty Subartini Betty Subartini Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Dwi Susanti Edi Kurniadi Emmanuel Parulian Sirait Estu Putri Dianti Ghazali, Puspa Liza Hasbullah, Soeryana Herlina Napitupulu Hukama, Atha Iin Irianingsih Jumadil Saputra Kahar, Ramadhina Hardiva kalfin Kalfin Kankan Parmikanti Khalilah Razanah Zakirah Komar Komar Linda Damayanti Putri Luki Setiawan Luki Setiawan Lutfi Praditia Ma’mur Maharani, Asthie Zaskia Ma’mur, Lutfi Praditia MIFTAAHUL JANNAH Moisino, Misel Lindi Nahda Nabiilah Noriszura Ismail Novianti, Saqila Pramudhita, Annisa Pryimak, Evgen Putri Adhira Novalia Putri Chaerunnisa Febryanti Putri, Aulya Putri, Linda Damayanti Qurrotu Aini Radya Pratiwi Serila Raharjanti, Amalia RAHMAWATI, SEPTI Ramdhania, Tya Shafa Ratih Kusumadewi Riadi, Nadia Putri Riza Adrian Ibrahim Saefullah, Rifki Silvia Wijaya Soeryana Hasbullah Subartiny, Betty Sudartianto Sudartianto Sukono Sukono Sukono Sukono Supian, Sudradjat Susanto, Sunarta Sya’imaa.HS, Audrey Ariij Tika Fauzia Tyrenia Rahmawati Ulfatmi, Ristifani Widyani, Azizah Rini Willen Vimelia Willen Vimelia Yasir Salih Yeremia Herry Parulian Yeremia Herry Parulian, Yeremia Herry Yudhi Andriyana Yulianus Brahmantyo Zahra, Ami Emelia Putri