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All Journal Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) Mathvision : Jurnal Matematika EIGEN MATHEMATICS JOURNAL Journal of Mathematics: Theory and Applications Jurnal Siger Matematika Al-Aqlu : Jurnal Matematika, Teknik dan Sains Papanda Journal of Mathematics and Sciences Research Parameter: Jurnal Matematika, Statistika dan Terapannya
Anugrawati, Sri Dewi
Universitas Islam Negeri Alaudddin Makassar
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Environmental Science Mathematics Medicine & Pharmacology

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Journal : EIGEN MATHEMATICS JOURNAL

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Stock Portfolio Optimization Using Single Index Model (SIM) with Exponentially Weighted Moving Average (EWMA) Approach Mutmainna, Ainul; Nurwahidah, Nurwahidah; Anugrawati, Sri Dewi
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.247

Abstract

The optimal portfolio is a combination of various assets with the aim of reducing investment risk through diversification. This study aims to conduct stock selection using K-Means Clustering and the formation of an optimal stock portfolio from the application of Single Index Model the amount of investment risk in the portfolio using the Exponentially Weighted Moving Average approach, and the amount of portfolio performance. The analysis results show that there are 5 portfolios formed. The best portfolio that can be chosen by investors depends on the investor's risk tolerance. Investors with low risk tolerance can choose Portfolio 3 consisting of ICBP and MIKA stocks with an expected return of 0.01343 and a risk of 0.00714 and a VaR of IDR 2,633,286.63. Investors with moderate risk tolerance can choose Portfolio 1 which consists of ICBP, MIKA, ACES, INCO, ITMG, MAPI, TPIA, AKRA, and MDKA stocks with an expected return of 0.022047, risk of 0.01277 and VaR of IDR 3,083,287.87. Investors with high risk tolerance can choose Portfolio 2 which consists of MIKA, TPIA, and MDKA stocks with an expected return of 0.02504 and a risk of 0.01471 and a VaR of IDR 3,553,167.10.
Penentuan Cadangan Asuransi Jiwa Last Survivor berdasarkan Metode Gross Premium Valuation (GPV) dengan Hukum De’Moivre Jefri, Rhanny Kirana; Anugrawati, Sri Dewi; Nurwahidah, Nurwahidah
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.326

Abstract

Insurance is one of the measures that can be used to prepare for various risks that can occur at any time. In the context of life insurance products, multiple life insurance is an efficient option because it is more economical than purchasing separate policies for two people with equivalent benefits. Unlike previous studies that focused on single life models using the GPV (Gross Premium Valuation) approach, this study develops an analysis of more complex multiple life insurance products, thereby providing a more representative picture of premium reserves for cases involving two insured parties. This study aims to formulate a mathematical model and conclude the results of prospective premium reserve calculations for last survivor whole life insurance using the GPV (Gross Premium Valuation) approach and De'Moivre's law De’Moivre This study uses a quantitative method with a documentation data collection technique, namely the 2019 Mortality Table IV data published by the Indonesian Life Insurance Association (AAJI). The results of this study show that the mathematical model of premium reserves for last survivor whole life insurance using the GPV (Gross Premium Valuation) approach and De'Moivre's law is ${_t}V^{GPV} = BA_{\bar{xy}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{xy}} + CA_{\bar{xy}} - G_{\bar{xy}}{\ddot{a}}_{\bar{xy}}$. However, when the insured ($y$) dies first, the mathematical model is ${_t}V^{GPV} = BA_{\bar{x}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{x}} + CA_{\bar{x}} - G_{\bar{xy}}{\ddot{a}}_{\bar{x}}$ while if the insured ($x$) dies first, the mathematical model is ${_t}V^{GPV} = BA_{\bar{y}} + U + PAG_{\bar{xy}} + A{\ddot{a}}_{\bar{y}} + CA_{\bar{y}} - G_{\bar{xy}}{\ddot{a}}_{\bar{y}}$. In addition, the results of the study show that there is a difference in the last survivor life insurance premium reserve between the conditions when both insured persons are still alive and when one of them dies, and that the use of De'Moivre's law results in a decreasing reserve pattern but ends up exceeding the promised benefits due to linear mortality assumptions so that the present value of the benefits does not fully decrease at the end of the coverage period. These findings indicate that the use of a uniform death distribution needs to be considered in order to produce more realistic premium reserves.
Co-Authors Abeng, Andi Tenri Adnan Sauddin Alwi, Wahidah ida Andi Mariani Anugrah, Sri Ayu Asriani Hasan Ermawati Ermawati Erna Fitrah Irwan Kasse Irwan, Muh. Ismawati Ismawati Iyut Wahyu Saputri Jefri, Rhanny Kirana Jusman Usman M Arlan Darmawan Muhammad Ihsan Salim Mutmainna, Ainul Nur Aeni Nurfadilah, Khalilah Nurhikma Nurul Anisha Dahlan NURWAHIDAH NURWAHIDAH Nurwahidah Nurwahidah Rahma Sri Susanti Sainal Abidin Enal Susanti, Rahma Sri Syarfiah, Syarfiah Wahidah Alwi Wahidah Alwi Wahyuni Abidin Yusrianto