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Ahmad Fuad Zainuddin
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INDONESIA
Indonesian Actuarial Journal
Published by Persatuan Aktuaris Indonesia
ISSN : -     EISSN : 31106463     DOI : -
Core Subject : Economy, Science, Education,
Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Physics
The Indonesian Actuarial Journal (IAJ) is an international peer-reviewed electronic journal published by the Society of Actuaries of Indonesia (Persatuan Aktuaris Indonesia). The journal is published twice a year and may also feature special issues addressing specific themes of interest in actuarial science and related fields. IAJ focuses on advancing theoretical and applied research in actuarial science and its interdisciplinary domains. The journal welcomes high-quality manuscripts that contribute to the development of actuarial theory, methodology, and practice, as well as studies with implications for policy, industry, and education. The scope of IAJ encompasses a wide range of topics, including but not limited to: life and non-life insurance mathematics, pension and social security systems, risk theory, health insurance, financial and investment modeling, applied probability and statistics, stochastic processes, and emerging areas in data analytics and actuarial applications. IAJ serves as a platform for researchers, practitioners, academics, policymakers, and students to exchange knowledge and insights that advance the actuarial profession both in Indonesia and globally.
Arjuna Subject : Matematika - Statistik dan Probabilitas
Articles 16 Documents
 1   2 
Analysis of the Health Social Security Administration (BPJS Kesehatan) Claim Amount using Random Forest Regression Andirasdini, Indah Gumala; Saputra, Desta; Rivai, Muklas; Putra, Septia Eka Marsha
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp001-008

Abstract

Claims paid by hospitals need to be identified to verify the accuracy of health services, maintain service quality, and optimize services provided to the Health Social Security Administration (BPJS Kesehatan) participants. This aligns with the third goal of the Sustainable Development Goals (SDGs), which is to ensure healthy lives and promote well-being for all ages, particularly in the context of universal health coverage. The difference in tariffs set by BPJS Kesehatan (INA-CBGs) compared to the amount paid by hospitals has led to a problem that can harm health facilities, such as delayed claim payments. This study aims to analyze the amount of claims paid by a regional hospital to BPJS Kesehatan participants using machine learning with the Random Forest Regression method. Based on this modeling, it was found that the severity of patients, length of stay, and type of illness are the most significant factors in determining the amount of claims. This study has an accuracy value of 81.89%, an adjusted R-square value of 80.4%, and a Mean Absolute Percentage Error (MAPE) of 18.11% in estimating the amount of claims.
Use of Actuarial Models for Determining Premiums and Reserves Soehardjoepri, Soehardjoepri; Azwarini, Rahmania
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp073-083

Abstract

Premium and reserve determination is a crucial aspect in the insurance industry, which ensures the ability of insurance companies to meet their obligations to policyholders and continue to operate sustainably. This study aims to explore the use of actuarial models in premium and reserve determination, focusing on classical models such as mortality and run-off models as well as modern techniques such as chain-ladder and Monte Carlo simulations. The data used includes historical information on claims and premiums from several leading insurance companies over the last five years. The research methodology involves data analysis using various actuarial models to estimate fair premiums and adequate reserves. The results of the analysis show that the use of appropriate actuarial models can produce more accurate premium estimates and more reliable reserves, compared to traditional approaches. In addition, the study found that the chain-ladder model and Monte Carlo simulation provide advantages in dealing with high claim variability. The findings of this study provide significant practical implications for insurance companies in managing risk and determining premium and reserve policies. The application of appropriate actuarial models can help insurance companies in improving financial stability and policyholder confidence. This study also suggests further research to explore the use of actuarial models in the context of climate change and other emerging risks.
Advancing Sharia Insurance Product for Natural Disaster Risks: A Collective Risk Model Approach Saragih, Trecy Elisabet Tioralina; Lintang, Alfonsius; Sinaga, Chintya Luminar
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp009-019

Abstract

Sharia insurance (takaful) serves as a means to promote solidarity and shared responsibility, helping protect individuals from unexpected risks by transferring or minimizing these risks through coverage provided by insurance companies. Sharia insurance is grounded in the concept of ta’awun which leads to mutual assistance and aims to eliminate forbidden elements in conventional insurance practices such as interest (riba), uncertainty (gharar), and gambling (maysir). Although interest rates are not used to calculate the present value of benefits, sharia insurance products can be improved through actuarial modelling based on expected risk levels and historical data. This paper creates a sharia insurance model for natural disasters of floods and earthquakes using the Collective Risk Model (CRM), with natural disaster frequency data distributed Poisson and natural disaster loss amounts distributed Weibull 3-Parameters. The result reflects the contribution value calculated using the expectation principle and standard deviation of total natural disaster losses. This study also provides a mathematical table as a model for applying the CRM’s contribution value to sharia insurance for natural disasters of floods and earthquakes. This table will detail how funds contributed by policyholders are managed, including the percentages allocated to personal accounts, the tabarru’ (donation) account, and ujrah (management fees), as well as the amounts of profit and benefits accrued to policyholders. This breakdown aims to promote transparency and fairness in shariah-compliant insurance for companies and policyholders, ensuring that fund contributions are managed equitably.
Modelling The Probability of Insurance Company’s Bankruptcy Using Integro-Differential Equation and Its Simulation Maulida, Ghafira Nur; Prabowo, Agung; Supriyanto, Supriyanto; Mamat, Mustafa; Sukono, Sukono
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp084-094

Abstract

Ruin is one of the risks that insurance companies may face. Therefore, modeling the probability of ruin is a crucial aspect of risk management. This study aims to model and analyze the probability of ruin in insurance companies using integro-differential equations, assuming that the claim size follows a mixtures of two exponential distributions. The research methods are literature study and numerical simulation with phyton. Numerical calculations were performed using Python programming, and the results are presented in tables and graphs to facilitate analysis. The model is applied to three different cases. The findings indicate that the probability of ruin is inversely proportional to the initial capital and premium loading, while it is directly proportional to the expected value of claims. In other words, the probability of ruin decreases significantly as the initial capital and premium loading increase, whereas it increases as the expected value of claims rises. Therefore, the greater the surplus of an insurance company, the lower the probability of ruin.
Application Of Annual Ratchet Method And Black-Scholes Model In The Calculation Of Single Net Premium Of Unit-Linked Endowment Life Insurance Magistrawati, Husnul Fausiah; Abdal, Ainun Mawaddah
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp020-032

Abstract

Given the dynamic market conditions, the calculation of a single net premium for unit-linked endowment life insurance becomes increasingly crucial to ensure a balance between life protection and potential investment returns. Insurance companies need to take into account market volatility and economic uncertainty in the premium setting process so that the products offered remain relevant and competitive in the eyes of the public. This research aims to calculate the net single premium value of unit-linked endowment life insurance using Annual Ratchet. It also aims to calculate the net single premium of unit-linked endowment life insurance using the Black Scholes model and aims to compare the calculation of net single premium of unit-linked endowment life insurance with the minimum benefit of the Annual Ratchet and Black Scholes methods using prospective calculations. There are two methods that will be used, namely the Annual Ratchet method and the Black-Scholes model. The results of the calculation of the net single premium of unit-linked endowment life insurance for the insured aged 40 years using the Annual Ratchet method for women amounted to Rp. 10,955,968 and men amounted to Rp. 13,725,243. While the results of the calculation of the single net premium of unit-linked endowment life insurance for the insured using the Black Scholes model for women amounted to Rp. 14,073,580 and men amounted to Rp. 17,672,045. The single net premium of unit-linked endowment life insurance for ages 45, 50, and 55 years shows an increase, both for women and men. This is due to the higher risk of death that makes the net single premium increase from year to year and the value of the investment plays a role.
Valuation of Pension Funds with Attained Age Normal and Projected Unit Credit Methods: Case Study of PT Taspen (Persero) Samarinda Branch Nur Auliya, Annisa; Indrawan, Indrawan; Azka, Muhammad
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp033-045

Abstract

The pension fund serves as a guarantee of an individual's economic welfare after retirement, providing pension benefits. Civil Servants are among the workers entitled to pensions managed by PT. Taspen (Persero). However, Civil Servants are often perceived as a financial burden on society, as the government’s pension scheme places a significant strain on the State Budget (APBN). Therefore, it is necessary to revise the scheme by conducting accurate actuarial calculations to reduce this burden. This research is intended to determine the normal contribution rates and actuarial obligations through the application of the Attained Age Normal and Projected Unit Credit methods at PT. Taspen (Persero) Samarinda Branch Office, with a 6% interest rate. The findings show that based on the Attained Age Normal approach, the normal contribution tends to rise as employees near retirement. In contrast, the Projected Unit Credit method provides a more consistent and evenly distributed contribution pattern throughout the working period. Regarding actuarial obligations, both methods demonstrate an upward trend; however, the Attained Age Normal method typically produces greater liabilities compared to the Projected Unit Credit method.
Forecasting Rupiah-to-US Dollar Exchange Rate 2020 - 2025 Using a Fuzzy Time Series Markov Chain Model Rahmadani, Tiur Masayu; Maeni, Rosa; Hwa, Camelia Miftahur Rizki Kiem; Khasanah, Iftha Nikmatul; Yeo, Winner; Alfarisi, Kgs. M. Rifat; Kurniawan, Yohana Joevanca; Juwono, Adriano Fadlan; Tauryawati, Mey Lista
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp060-072

Abstract

The exchange rate of the Indonesian Rupiah against the US Dollar experiences frequent fluctuations, making economic forecasting and financial planning more difficult. This study aims to enhance exchange rate prediction accuracy by combining Fuzzy Time Series with Markov Chain probability transitions. The approach is grounded in the idea that probabilistic modeling of state changes improves the representation of dynamic currency behavior. Using daily IDR/USD data from April 2020 to March 2025, the methodology involves two main steps: fuzzifying historical exchange rate data into linguistic variables, and applying a Markov Chain to compute transition probabilities between these fuzzy states. The model’s forecasting accuracy is evaluated using mean absolute percentage error. Results show that the hybrid model achieves a lower error rate of 0.50%, compared to 0.61% using conventional Fuzzy Time Series alone. This demonstrates the hybrid model’s ability to capture both sudden market changes and stable patterns effectively. The findings suggest that the integration of Markov Chain transitions significantly improves the predictive performance of fuzzy-based models. In conclusion, this hybrid method provides a practical and reliable forecasting tool for financial analysts and policymakers. Future research could include additional economic indicators and explore alternative probability weighting methods to further enhance model accuracy.
Development of Economic Capital Using Value-at-Risk (VaR) for Catastrophe (Re)Insurance -, Danar Handoyo; -, Rahmalia Falah Anwar; Damanik, Ruben; Nainggolan, Rico Fernando
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no1pp046-059

Abstract

Effective risk management requires robust risk quantification by integrating a company’s aggregate risk exposures. This approach strengthens risk awareness and informs mitigation strategies for stakeholders. This study explores economic capital as a framework for assessing risk-based capital requirements, specifically focusing on catastrophe risk in (re)insurance firms. The proposed risk quantification framework utilizes the Value-at-Risk (VaR) methodology to statistically estimate potential losses at predetermined confidence intervals. To address the inherent complexity of catastrophe risks, the model incorporates sophisticated distribution modeling and stochastic simulation techniques. These advanced analytical approaches are implemented through specialized catastrophe modeling platforms to optimize capital adequacy evaluations. This framework ensures financial resilience against extreme stress scenarios by implementing VaR at a predetermined threshold. The findings support management in optimizing capital allocation, risk controls, and mitigation strategies while balancing profitability and risk exposure.
Precision-Oriented Churn Prediction with a Fine-Tuned Meta-Learner Stack Model and SHAP: A Case Study on IBM Telco Ghaza Antani, Tajmahal; Hakim, Adhan Haidar; Nurrizky, Rayna; Annelia Einstania Vyorra, Venny; Septyanto, Fendy
Indonesian Actuarial Journal Vol. 1 No. 2 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no2pp137-151

Abstract

Customer churn prediction is essential in the telecommunications industry, where maintaining existing customers is significantly more cost-effective than acquiring new ones. This study introduces a precision-oriented stacked ensemble model to predict churn using the IBM Telco Customer Churn dataset. Emphasis is placed on maximizing precision to reduce false positives, thereby minimizing unnecessary and costly intervention efforts. The proposed architecture employs LightGBM, CatBoost, and Logistic Regression as base learners, with a fine-tuned ElasticNet serving as the meta-learner. Evaluation results show that the stacking model achieves strong overall performance, attaining an AUC of 0.917 and the highest precision among all models tested. To ensure interpretability, SHapley Additive exPlanations (SHAP) are applied to identify key drivers of churn such as number of referrals, contract type, monthly charges, and tenure. These findings demonstrate that a precision-focused approach can balance business efficiency and predictive power, offering a robust framework for proactive and cost-sensitive churn management.
Catastrophe Reinsurance Single Premium Valuation Model Based on Indonesia's Earthquake Data Nurtanio, Priscilla Natalie; Realino, Pieter; Sugiarto, Temmy; Nathaniel, Darren; Tjandra, Raymond; Angelina, Theresa; Nafiputra, Arzu; Lukman, Dave Filbert Iglesias
Indonesian Actuarial Journal Vol. 1 No. 2 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol01no2pp113-127

Abstract

Indonesia's position along the Pacific Ring of Fire makes it highly vulnerable to catastrophic earthquakes, creating significant financial exposure for insurers through simultaneous surges in life, health, and property insurance claims.  This study develops a comprehensive valuation model for catastrophe reinsurance contracts using advanced statistical techniques to assess extreme risks and their interdependencies. The model integrates three key approaches: (1) the Peaks Over Threshold method with Generalized Pareto Distribution to analyze extreme losses from fatalities and injuries, (2) copula theory (Clayton and Gumbel) to capture dependence structures between different claim types, and (3) Monte Carlo simulations to project future event frequencies and financial impacts. Using Indonesian seismic data from 1979 to 2025 while excluding extreme outlier events, we model extreme losses in fatalities and injuries. While also employing the Fundamental Theorem of Asset Pricing to determine reinsurance premiums as the expected present value of potential claims. , with the Gumbel copula demonstrating superior fit for upper-tail dependence between variables. The model implements realistic assumptions, including: a retention limit of Rp15 billion for the primary insurer, average claims of Rp500 million per life and Rp15 million per injury, and coverage of 5% and 7% of the population for life and health policies, respectively. Applying a 5.75% discount rate (BI rate 2025) through 10,000 Monte Carlo simulations, we calculate a single reinsurance premium of Rp17,395,932,554. The results demonstrate how advanced statistical methods can effectively quantify catastrophe risk transfer, providing insurers with an actuarially sound pricing framework for managing low-frequency, high-severity earthquake exposures. However, a limitation of this study includes the exclusion of the 2004 mega-disaster, which may lead to an underestimation of worst-case scenarios, and the use of fixed assumptions for insurance coverage and claim values, which may not fully reflect real-world variability. Despite these limitations, this approach offers a valuable framework for managing earthquake-related risks in Indonesia’s reinsurance market.

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