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All Journal JBIO: jurnal biosains (the journal of biosciences) CAUCHY: Jurnal Matematika Murni dan Aplikasi Althea Medical Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Zero : Jurnal Sains, Matematika, dan Terapan Jambura Journal of Mathematics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika GREENOMIKA Jurnal Kesehatan Jurnal Pendidikan Administrasi Perkantoran (JPAP) Milang Journal of Mathematics and Its Applications Jurnal Indonesia Sosial Sains Proceeding Applied Business and Engineering Conference MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
Retno Budiarti
Program Study Of Actuary, School Of Data Science, Mathematics And Informatics, IPB University, Indonesia
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Analysis of Ruin Probability in Insurance Companies Using the Cramer-Lundberg Model with Variations in Claim Distributions Alfi Khairiati; Retno Budiarti; Mohamad Khoirun Najib
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.25581

Abstract

Ruin risk is a critical concern in the insurance industry, reflecting a company's ability to fulfill long-term claim obligations. This study estimates ruin probabilities using the Cramer-Lundberg model, with Monte Carlo simulation applied to three claim distributions: exponential, lognormal, and gamma. Simulations vary initial capital while holding the premium rate, claim intensity, and distribution parameters constant. Results show that the lognormal distribution, due to its heavy tail, leads to higher ruin probabilities compared to exponential and gamma distributions. The gamma distributions produce intermediate outcomes, while the exponential shows the lowest risk. These findings highlight the importance of considering distributional characteristics when assessing solvency risk. The study provides practical insights for actuaries and risk managers in evaluating capital adequacy, stress-testing portfolios, and developing adaptive pricing and reinsurance strategies.
PENENTUAN PORTOFOLIO SAHAM DI INDONESIA DENGAN MEMAKSIMUMKAN SHARPE RATIO Retno Budiarti; Nur Agustiani; Muhammad Ariq Rizky; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 2 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.2.179-189

Abstract

Investasi saham telah menjadi instrumen keuangan yang banyak dimanfaatkan untuk meraih keuntungan dalam jangka panjang. Namun, volatilitas harga saham yang fluktuatif dan volatil menuntut pentingnya manajemen risiko dalam penyusunan portofolio. Penelitian ini bertujuan menyusun portofolio optimal melalui maksimisasi Sharpe Ratio dengan memanfaatkan hasil clustering sebagai dasar seleksi saham. Data yang digunakan meliputi hasil clustering dari 700 saham  di Bursa Efek Indonesia (BEI), dikelompokan berdasarkan karakteristik return dan volatilitas. Selanjutnya, dipilih saham-saham dominan yaitu saham dengan return tertinggi dan volatilitas terendah, dari setiap cluster, lalu dianalisis kombinasi saham dengan korelasi rendah untuk membentuk portofolio. Alokasi bobot saham dalam portofolio ditentukan melalui proses optimisasi Sharpe Ratio. Temuan penelitian mengungkapkan bahwa portofolio optimal cenderung memberikan porsi bobot lebih besar kepada saham-saham dengan return tinggi dan volatilitas rendah. Sebaliknya, portofolio yang terdiri dari saham dengan karakteristik return dan volatilitas serupa menunjukkan distribusi bobot yang lebih merata, namun menghasilkan nilai Sharpe Ratio yang lebih rendah dibandingkan portofolio yang mengombinasikan saham dengan karakteristik berbeda. Kata kunci: Clustering, investasi, portofolio saham, pengelolaan risiko, Sharpe Ratio
ASYMPTOTIC DISTRIBUTIONS OF ESTIMATORS FOR THE MEAN AND THE VARIANCE OF A COMPOUND CYCLIC POISSON PROCESS Ika Reskiana Adriani; I Wayan Mangku; Retno Budiarti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0453-0464

Abstract

A stochastic process has an important role in modeling various real phenomena. One special form of the stochastic process is a compound Poisson process. A compound Poisson process model can be extended by generalizing the corresponding Poisson process. One of them is using a cyclic Poisson process. Our goals in this research are to determine the asymptotic distribution of the estimator for the mean and the variance of this process. In this paper, the problems of estimating the mean function and the variance function of a compound cyclic Poisson process are considered. We do not assume any parametric form for the intensity function except that it is periodic. We also consider the case when only a single realization of the cyclic Poisson process is observed in a bounded interval. Consistent estimators for the mean and variance functions of this process have been proposed in respectively. This paper introduces a set of novel theorems that, to the best of our knowledge, are not available in the existing literature and contribute original results to the field. Asymptotic distributions of these estimators are established when the size of the observation interval indefinitely expands. Asymptotic distributions of and are, respectively and as .
GENERALIZED NESTED COPULA REGRESSION TO UNVEIL THE IMPACT OF EXCHANGE RATES AND NIKKEI 225 ON BANK MANDIRI STOCK PRICE Alfi Khairiati; Retno Budiarti; Mohamad Khoirun Najib
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1167-1184

Abstract

Fluctuations in exchange rates and foreign stock indices strongly influence domestic stock performance, particularly in the banking sector, which is highly sensitive to global economic dynamics. Traditional financial models often fail to capture the complex, non-linear dependencies between these variables, underscoring the need for more advanced approaches. This study examines the effectiveness of copula-based regression models in predicting Bank Mandiri’s (BMRI) stock price using exchange rates and the Nikkei 225 Index as predictors. Conventional regression methods, such as Linear Regression, cannot adequately capture nonlinear relationships and tail dependencies in financial time series. To address this, we compare Elliptical Copula, Symmetric Archimedean Copula, Asymmetric Archimedean Copula, and Generalized Nested Copula models. Results show that the Generalized Nested Copula Regression achieves the lowest Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Weighted MAPE (wMAPE), effectively modeling asymmetric and tail dependencies that are crucial in financial forecasting. While Elliptical Copula (t-Copula) also provides strong predictive accuracy, Archimedean copulas perform poorly, failing to improve upon linear regression. These findings highlight the importance of flexible statistical models in financial prediction, demonstrating that copula-based regression offers a superior alternative to traditional methods. Unlike prior research that often relied on simpler copula families or linear models, this study introduces a Generalized Nested Copula Regression in the context of the Indonesian banking sector, addressing a gap in emerging market literature. The study assumes correctly specified marginal distributions and a stable dependency structure, which may limit applicability under rapidly changing market conditions. Future work should consider dynamic copula structures and additional economic indicators to further enhance predictive accuracy.
Mathematical Model of Joint Life Term Insurance Premiums under Inflation, Interest Rate, and Dependent Mortality Ine Febrianti Habel; I Gusti Putu Purnaba; Retno Budiarti
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.35690

Abstract

Multilife insurance refers to a contract that covers two or more lives simultaneously, with joint life insurance representing a key form in which the benefit is paid upon the first death among the insured individuals. The lifetimes of insured individuals are typically not independent, as they may be influenced by shared environmental, health, or behavioral factors, leading to mortality dependence. Inflation and interest rates also play critical roles in determining the present value of benefits and premiums. However, most previous studies have examined either mortality dependence or macroeconomic effects in isolation. This study aims to develop a comprehensive mathematical model for determining joint life term insurance premiums that simultaneously incorporates mortality dependence through the Gumbel copula and interest rate and inflation through the Fisher equation. The model integrates demographic and economic risk components within a unified actuarial valuation framework, providing a more realistic representation of premium dynamics under varying financial conditions. Simulation results indicate that premiums incorporating inflation are consistently higher than those without inflation, whereas higher nominal interest rates result in lower premium levels. These findings reflect the theoretical relationship between inflation, real interest rates, and the time value of money. The study further introduces an elasticity-based analysis that quantifies the sensitivity of premiums to changes in inflation and interest rates, demonstrating nonlinear yet economically meaningful responses across different age structures of insured spouses. The results highlight the importance of jointly modeling mortality dependence and economic variables to enhance pricing accuracy and fairness in life insurance. The proposed model offers practical relevance for actuaries in premium determination, assists insurers in risk management and product design, and supports the development of resilient pricing strategies under inflationary and interest.
Modelling The US Dollar Index Using Continuous Hidden Markov David Vijanarco Martal; Berlian Setiawaty; Retno Budiarti
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1986

Abstract

This study employs the continuous hidden Markov model (HMM) to model the index data of the US Dollar index from 2018 to 2024. HMM is used to predict and analyze hidden patterns that generated the data. The data is modelled using a continuous HMM with 11 hidden states and lognormal distributions with different parameters for each hidden state. The accuracy of the continuous HMM is measured by MAPE. The MAPE value for both training and testing data is very low, less than 4%. This means that the continuous HMM can be used to model the data accurately. The plot shows accurate predictions between simulated data and real data, and furthermore, the model can capture the fluctuations of the data.
Co-Authors Ade Irawan Aldinasyah, Monicha Zalzabilla Alfi Khairiati Alfi Khairiati Anang Kistyanto Andre Dwijanto Witjaksono Asri Rahmawati Berlian Setiawaty Bib Paruhum Silalahi Chalimatusadiah Chalimatusadiah D. S. Rahmawati Daniel Happy Putra Dara Irsalina David Vijanarco Martal David Vijanarco Martal Dewi, Komang Nonik Afsari Diana, Adawiyah Putri Donny Citra Lesmana Dwi Fidiana Endar Hasafah Nugrahani Erliana, Windiani Fendy Septyanto Garianto, Efyluk Grifin Ryandi Egeten Hadi Sumarno Hantrisa Nurrizki Helynda Mulya Arga Retha Helynda Mulya Arga Retha Hemarani, Febri Herdiyantini, Mita I Gusti Putu Purnaba I Wayan Mangku Ika Reskiana Adriani Ine Febrianti Habel Intansari, Kumala Khairiati, Alfi Khan, Joan Kurniadi Rizki Lusiana Sani Parwati Manjaruni, Vivin Aprilia Mohammad Reza Muhammad Ariq Rizky Muhammad Yusuf Sulaiman Mulyasari, Rindi Melati Najib, Mohamad Khoirun Nashiruddin, Muhammad Abdurrasyid Nefertiti, Eva Nur Agustiani Nur Agustiani Nur Agustiani Prasetya, Hanung Priambodo, Bima Putra, Hilman Yusupi Dwi Putra, Oki Nugraha Rafhida, Syukri Arif Rahadianto, Rahadianto Rahmah, Salsabilla Rahmawati, D. S. Rizki, Kurniadi Ronald Pratama Adiwinoto Ruhiyat Ruhiyat S. Soedarsono Setyawan, Binar Aulia Silalahi, Romaito Br siswadi - SISWANDI, S. Sitepu, Sanfriska Br Sri Nurdiati Sudiarta, Ketut Edy Sulaiman, Muhammad Yusuf Syukri Arif Rafhida Titut Harnanik Utami, Nadila Rizqi Wa Ode Intan Fully Nadya Windiani Erliana Yulianty, Sherly