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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 24 Documents
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Identifying Weakly Correlated Dominating Stocks using Maximum Independent Set Gimanjar, Yeremia Bertolla; Prastiwi, Diah; 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/iajvol01no2pp128-136

Abstract

In this paper we consider the problem of efficiently finding a (small) set of stocks taken from an index that can replicate the index performance. Furthermore, we add the requirement that the set’s returns have weak correlation with each other. Such a selection of stocks may be useful for investors who want to simplify their analysis of the stock index, trying to capture market movement with reduced risk. To solve this problem, we use maximum independent set, a concept from graph theory. As a case study we consider IDX80 in the year 2024.
Cost Component Calculation for Endowment Insurance Premiums on Multiple Life Using the Gompertz Distribution Febrisutisyanto, Ady; Haryanto, Dwi; Damara, Antonia Samantha
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/iajvol01no2pp152-163

Abstract

This study aims to develop a gross premium model for endowment insurance products under a multiple life setting by incorporating various actual cost components and applying the Gompertz mortality distribution. The proposed model includes acquisition costs at the beginning and end of the first policy year, premium collection costs, and annual policy maintenance costs, all of which are calculated based on present values of benefits and annuities. Parameter estimation is conducted using linear regression with a bounded optimization approach, where all parameters are constrained to be strictly positive to reflect realistic conditions in insurance practice. The simulation results yield parameter estimates of  a1=0,97074,  a2=0,912217, β=Rp 19.344,46 and γ=Rp 20.105,23 which are considered actuarially reasonable. The high coefficient of determination, , R2=98,46%, indicates that the model has an excellent fit to the gross premium data. This research demonstrates that an actuarial-based cost formulation combined with statistical estimation can serve as an effective and transparent approach in determining premiums for endowment life insurance products with more than one insured.
A Deeper Look Into an Insurance Risk Model with Two Types of Claims and FGM Copula Dependency Saruan , Sandy Salomo; Effendie, Adhitya Ronnie
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/iajvol01no2pp095-112

Abstract

This paper investigates a continuous-time, two types of claims risk model where the dependence between claim sizes and inter-claim times is structured using a Farlie–Gumbel–Morgenstern (FGM) copula. The methodology begins with the construction of a Lundberg’s equation and the determination of its non-negative roots. Subsequently, the integro-differential equation for the ruin probability is derived, from which the Laplace transform of the ruin probability is obtained. For the specific case of exponentially distributed claim sizes, an explicit analytical expression for the ruin probability is derived to examine the effects of dependence parameters and distributional characteristics. A series of numerical experiments with varying FGM copula parameters demonstrate that the ruin probability decreases as the initial surplus increases and is significantly influenced by the strength of the dependence structure. From a practical perspective, distinguishing between claim types allows insurers to identify which category poses the greatest threat to solvency, thereby supporting more targeted underwriting and accurate capital allocation strategies.
Comparison of Estimation Methods for the Weibull Distribution in Indonesian Life Tables Alibazah, Terra Dei; Prabowo, Agung
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/iajvol01no2pp185-202

Abstract

This study evaluates the performance of the Ordinary Least Squares, Nonlinear Least Squares, and Maximum Likelihood Estimation methods in fitting the two parameter Weibull distribution to the 2019 Indonesian Life Table and the 2023 Indonesian Population Life Table, focusing on ages 59-111. The lower age bound is selected to isolate the adult and late-life mortality in which the Weibull model’s assumptions are most applicable. Although both life tables exhibit monotonically increasing mortality with the same terminal age, they differ in the age at which mortality acceleration becomes pronounced. Goodness-of-fit was assessed through a comparison of root mean squared errors, root mean squared logarithmic errors, and residual plots. The results indicate that the Ordinary Least Squares method, while computationally stable, tends to overestimate survival beyond the terminal age. The Nonlinear Least Squares method better aligns with the empirical survival yet similarly extends the terminal age. The Maximum Likelihood Estimation method provides more realistic terminal ages but inflates survival at infancy and midlife stages. These findings highlight that estimation methods and data segment selection strongly influence the reliability of Weibull-derived life tables. Applications in actuarial and demographic practices require improved estimation strategies to better capture late-age mortality.
Analysis of JIBOR Discontinuity: Comparison of Spread Adjustment for Several Alternative Reference Rates for 1-Month JIBOR Zulfikar, Harly; Taufiq, Afif Amrullah; Giyatno, Among
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/iajvol01no2pp164-174

Abstract

The planned discontinuation of the Jakarta Interbank Offered Rate (JIBOR) publication by Bank Indonesia, effective January 1, 2026, has significant implications for the financial industry, particularly for life insurance contracts that reference JIBOR. Therefore, a credible and economically equivalent Alternative Reference Rate is needed. This paper addresses the discontinuity from two perspectives, forecasting methods for accurately predicting JIBOR post-discontinuation and analyzing the transition to four Alternative Reference Rates: Indonesia Overnight Index Average (IndONIA), BI Rate, LPS Rate, and the average deposit rate of state-owned banks (Bank Himbara). The methodology involves historical data analysis over the past five years, following the National Working Group on Benchmark Reform (NWGBR) recommendations. Findings show that for forecasting, the Autoregressive Model with Box-Cox transformation has the smallest error compared to actual JIBOR. Among Alternative Reference Rates, IndONIA has the smallest error compared to actual JIBOR. This paper is expected to provide insights for financial industry stakeholders affected by the JIBOR discontinuity, including insurance products using JIBOR as a Reference Rate in cash value calculations
Investment-Risk Protection Rider for Unit-Linked Insurance Gunawan, Kenneth; Margaretha, Helena; Winayaka, Yoseph Wastu
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/iajvol01no2pp175-184

Abstract

This paper designs an investment-risk protection rider that provides annual return bounds (a floor and a cap) at no explicit cost to the policyholder. The study models two scenarios using the Indonesia Stock Exchange Composite Index (IHSG) as the underlying asset: the first assumes the availability of derivative options to form a zero-cost collar, while the second assumes no options are available, forcing the company to use delta-neutral dynamic hedging. A primary novelty of this research is the demonstration of theoretical option pricing on non-normal return assets and the formulation of a "Semi Non-homogenous Double-Exponential Jump Diffusion" (SNDEJD) model, which is developed to resolve an analytical calculation issue found in the original Non-homogenous Double-Exponential Jump Diffusion (NDEJD) model's pricing formula, thereby allowing for theoretical option pricing while capturing long-term parameter shifts. The study concludes that if options are available, the rider is highly viable, offering a 0% return floor and a median cap of 14.9% with no risk to the insurer. However, the delta-neutral dynamic hedging approach is found to be ineffective and risky, as the Black-Scholes hedging model fails to cover the jump risks in the non-normal IHSG returns, leaving the company exposed to significant losses unless a much lower cap is set.
Measuring Risk Aversion Behavior Using Szpiros Approach: Case Study in Indonesias Life Insurance Industry Kristio Rapi; Dominicus Savio Priyarsono; Siti Jahroh; Toni Bakhtiar
Indonesian Actuarial Journal Vol. 2 No. 1 (2026): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol2no1pp001-012

Abstract

Life insurance industry shows promising benefits for Indonesia's economic and social sector, yet its penetration continues to decrease since 2016 despite income growth. This study addresses the phenomenon by analyzing the risk preference of Indonesian consumers using Szpiro's approach to measure risk aversion, then analyzes the effect of risk aversion on life insurance demand in Indonesia. We use data from Indonesia Insurance Statistics from 2006 to 2022 with annual period. Stationarity tests were conducted before time series estimation, Ordinary Least Square is used to estimate time series data, and Klein's rule is used to address multicollinearity problem in regression analysis. Evidence is presented in support of the positive effect of risk aversion on life insurance demand. The degree of relative risk aversion in Indonesia is estimated at 0.0915 with risk aversion value in 2022 of 0.1402, indicating that Indonesian people is a risk-averse individuals. Therefore, given the fact that Indonesia is a non-high-income country with risk-averse consumers, the opportunity to enhance life insurance demand remains open. This finding will help insurers in demand and pricing analysis.
Portfolio Optimization and Risk Estimation of LQ45 Mining Stock Using The ARIMA-GARCH-EVT-COPULA Hybrid Model as Alternative Pension Fund Investment Dyah Ayu Mahanani; Galuh Oktavia Siswono; Ulil Azmi
Indonesian Actuarial Journal Vol. 2 No. 1 (2026): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol2no1pp096-111

Abstract

Economic uncertainty and high commodity market volatility demand more accurate pension fund investment risk management. This study aims to measure risk and determine the optimal portfolio of LQ45 mining stocks as an alternative pension fund investment instrument using a hybrid GARCH-EVT-Copula approach. The data used are daily log returns of ITMG, ADRO, and PTBA stocks for the period June 1, 2020, to June 30, 2025. The ARIMA-GARCH model is used to capture volatility dynamics, while extreme risks are modeled using the EVT approach. Dependencies between stocks are analyzed using the best copula model and Monte Carlo simulations to produce VaR and ES estimates which are then validated using Backtesting. The results show that the best model for ITMG stocks is ARMA(0,0)-GARCH(1,1), for ADRO stocks it has an ARMA(1,1)-GARCH(1,1) model, and for PTBA stocks it has an ARMA(0,1)-GARCH(0,1) model. Based on the EVT estimation, ITMG and ADRO stock have positive GPD shape parameters, indicating a sfat-tailed distribution and a higher potential for extreme risk. In contrast, PTBA stock have negative shape parameters, indicating a limited tail distribution so that extreme risk is relatively more controlled. The scale parameter value also confirms that PTBA's extreme fluctuations are more stable than other stock. The portfolio dependency structure can be modeled using the best copula model, namely the Gumbel Copula, the optimization results give portfolio A a weight of 62.11456% for ITMG stock and 37.88544% for ADRO stock, portfolio B is 19.93126% for ITMG stock and 80.06874% for PTBA stock, while portfolio C is 8.668356% for ADRO stock and 91.33164% for PTBA stock. The results also show that the estimated VaR values ​​obtained are valid at all confidence levels, and the optimal portfolio tends to place PTBA and ITMG stock as dominant stocks to reduce the total portfolio risk. Thus, the ARIMA-GARCH-EVT-Copula approach is proven to be effective in modeling extreme risks and dependency structures between stocks, and can provide a strong basis for making long-term investment decisions for pension fund management.
Stochastic Multi-State Modeling for Critical Illness Insurance With Integration of Non-Homogeneous Trends and Pandemic Shocks Kenneth Gunawan; Helena Margaretha; Yoseph Wastu Winayaka
Indonesian Actuarial Journal Vol. 2 No. 1 (2026): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol2no1pp081-095

Abstract

This study develops a stochastic pricing framework for critical illness insurance using Indonesian population data. The framework captures the joint effects of mortality, morbidity, and longevity across age and sex. A multi-state model is constructed to represent transitions between one healthy state, eleven critical illness states, and death. Benefits are payable upon the first occurrence of a critical illness, upon death, and upon survival to age 95. Using publicly available incidence, prevalence, and mortality data, transition intensities are derived and projected to reflect future health risk patterns. Particular attention is given to the construction of transition intensities for first-time critical illness events under limited data availability. Pandemic-related mortality distortions are addressed through adjustment procedures, and the age domain is segmented to accommodate non-homogeneous mortality trends. Projection models are selected from seven stochastic mortality models based on performance criteria, and additional noise smoothing is applied when cohort-based models produce unstable projections. The results show that total expected costs for males and females are generally comparable. However, differences remain across age groups and benefit components. These findings support the use of age- and sex-specific pricing structures in critical illness insurance.
Estimation of Ruin Probabilities in an Extended Risk Model with Inhomogeneous Claim Counts and Financial Risks Nyanumba Walter Motanya; Oduar D. Brian; Joseph O. Nyakinda
Indonesian Actuarial Journal Vol. 2 No. 1 (2026): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.65689/iajvol2no1pp040-051

Abstract

Classical ruin models commonly assume stationary claim arrivals and often examine financial conditions, taxation, and heavy-tailed losses separately. This fragmentation limits their ability to assess insurer solvency when claim frequency and economic conditions vary simultaneously. This study develops an extended risk framework that jointly incorporates an inhomogeneous Poisson claim-counting process, financial adjustment through the real force of accumulation, and proportional taxation. Ruin probabilities are examined under exponential and subexponential claim-size distributions. For exponential claims, the framework provides an analytical characterization of the effects of initial surplus, premium loading, financial adjustment, and taxation on insolvency risk. For subexponential claims, the asymptotic analysis shows that ruin is governed by the tail behaviour of exceptionally large losses. The results indicate that larger initial reserves and premium loadings strengthen solvency, whereas higher claim intensity and taxation increase ruin risk; heavy-tailed claims also produce more persistent insolvency exposure than light-tailed claims. The novelty of the study lies in integrating time-varying claim arrivals, financial risk, taxation, and contrasting claim-tail regimes within a single analytical structure. The proposed framework provides a basis for solvency assessment, capital planning, and actuarial risk management under changing insurance and economic conditions.

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