Indonesian Actuarial Journal
type: channel
description: The Indonesian Actuarial Journal (IAJ) is published by the Society of Actuaries of Indonesia (Persatuan Aktuaris Indonesia). It is a journal dedicated to the development of actuarial science. It covers both theoretical and applied mathematical methods. The boundaries of actuarial mathematics are defined by the area of application rather than the uniformity of methods and techniques. Therefore, a paper of interest to the Indonesian Actuarial Journal (IAJ) may have its theoretical basis in actuarial science, probability theory, statistics, operations research, numerical analysis, data science, mathematical economics, or any other area of applied mathematics. The main criterion is that the paper should have specific relevance to actuarial applications. The Indonesian Actuarial Journal (IAJ) is published two times a year, in July and December.
publisher: Persatuan Aktuaris Indonesia
language: en
publication name: Indonesian Actuarial Journal
issn: 3110-6463
items: Stochastic Multi-State Modeling for Critical Illness Insurance With Integration of Non-Homogeneous Trends and Pandemic Shocks
items: Multiple Decrement Modeling of BPJS Health Transitions Under Air Pollution Exposure in DKI Jakarta
items: Government Employees with Employment Agreements Pension Fund Valuation Across 17 Salary Grades Using Entry Age Normal and Projected Unit Credit
items: Robust E-Bayesian Estimation and Prediction of Esscher Premium for Car Insurance Claim Frequencies Under a Negative Binomial Model
items: Forecasting and Financial Risk Analysis Using ARIMA Intervention Model: A Case Study on JMAS Tbk
items: Estimation of Ruin Probabilities in an Extended Risk Model with Inhomogeneous Claim Counts and Financial Risks
items: Portfolio Optimization and Risk Estimation of LQ45 Mining Stock Using The ARIMA-GARCH-EVT-COPULA Hybrid Model as Alternative Pension Fund Investment
items: Measuring Risk Aversion Behavior Using Szpiros Approach: Case Study in Indonesias Life Insurance Industry
items: Comparison of Estimation Methods for the Weibull Distribution in Indonesian Life Tables
items: Investment-Risk Protection Rider for Unit-Linked Insurance
items: A Deeper Look Into an Insurance Risk Model with Two Types of Claims and FGM Copula Dependency
items: Analysis of JIBOR Discontinuity: Comparison of Spread Adjustment for Several Alternative Reference Rates for 1-Month JIBOR
items: Modelling The Probability of Insurance Company’s Bankruptcy Using Integro-Differential Equation and Its Simulation
items: Application Of Annual Ratchet Method And Black-Scholes Model In The Calculation Of Single Net Premium Of Unit-Linked Endowment Life Insurance
items: Identifying Weakly Correlated Dominating Stocks using Maximum Independent Set
items: Cost Component Calculation for Endowment Insurance Premiums on Multiple Life Using the Gompertz Distribution
items: Development of Economic Capital Using Value-at-Risk (VaR) for Catastrophe (Re)Insurance
items: Forecasting Rupiah-to-US Dollar Exchange Rate 2020 - 2025 Using a Fuzzy Time Series Markov Chain Model
items: Catastrophe Reinsurance Single Premium Valuation Model Based on Indonesia's Earthquake Data
items: Precision-Oriented Churn Prediction with a Fine-Tuned Meta-Learner Stack Model and SHAP: A Case Study on IBM Telco
items: Valuation of Pension Funds with Attained Age Normal and Projected Unit Credit Methods: Case Study of PT Taspen (Persero) Samarinda Branch
items: Advancing Sharia Insurance Product for Natural Disaster Risks: A Collective Risk Model Approach
items: Use of Actuarial Models for Determining Premiums and Reserves
items: Analysis of the Health Social Security Administration (BPJS Kesehatan) Claim Amount using Random Forest Regression

Stochastic Multi-State Modeling for Critical Illness Insurance With Integration of Non-Homogeneous Trends and Pandemic Shocks
type: item
description: 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.
subject: Articles
  topic: section
subject: Financial services
  topic: keywords
subject: Critical Illness Insurance
  topic: keywords
subject: Stochastic Modelling
  topic: keywords
subject: Multiple State Model
  topic: keywords
subject: Mortality and Morbidity Projections
  topic: keywords
creator: Kenneth Gunawan
creator: Helena Margaretha
creator: Yoseph Wastu Winayaka
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 081
ending page: 095
doi: 10.65689/iajvol2no1pp081-095

Multiple Decrement Modeling of BPJS Health Transitions Under Air Pollution Exposure in DKI Jakarta
type: item
description: Air pollution represents a significant environmental health burden in Indonesia. Despite this, the quantitative relationship between ambient pollutant concentrations and population-level health state transitions within Indonesia’s national health insurance system remains uncharacterized. This study estimates cause-specific forces of decrement for health state transitions within the BPJS Kesehatan administrative claims data from DKI Jakarta spanning 2022 to 2024, and examines the association between ambient air pollutant concentrations and estimated transition intensities through exploratory LASSO regression. The analytical dataset comprises 454,001 FKTP and 147,379 FKRTL episodes, stratified by five-year age bands and calendar quarter. Multiple decrements across both care settings are modeled, with the FKTP-to-FKRTL referral (rujuk lanjut) decrement serving as the primary focus. NO2 emerged as a candidate predictor in exploratory screening, appearing with a positive coefficient in 6 of 17 age bands, with model-implied elasticities ranging from 0.063 to 0.544. Scenario analysis showed that a hypothetical 20% increase in ambient NO2 corresponded to fitted referral intensity increases of between 1.3 and 10.9 percent across retained age bands.
subject: Articles
  topic: section
subject: Air Pollution
  topic: keywords
subject: BPJS Kesehatan
  topic: keywords
subject: Force of Decrement
  topic: keywords
subject: FKTP
  topic: keywords
subject: FKRTL
  topic: keywords
creator: Bernadeth Saskia Laudya Cintya
creator: Leyton Raynaldo Ozzora
creator: Helena Margaretha
creator: Ferry Vincenttius Ferdinand
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 024
ending page: 039
doi: 10.65689/iajvol2no1pp024-039

Government Employees with Employment Agreements Pension Fund Valuation Across 17 Salary Grades Using Entry Age Normal and Projected Unit Credit
type: item
description: Accurate calculation of pension funds for Government Employees with Employment Agreements (PPPK) is crucial for the sustainability of the program. Variations in the age and age of entry used can result in significantly different pension cost projections, so a comprehensive analysis is needed to determine the right methods and assumptions. This study aims to analyze the differences in the calculation of present value future benefits, normal contributions, actuarial obligations, and lumpsum benefits by taking into account based on class and age of entry. This quantitative research uses actuarial simulations using the Entry Age Normal (EAN) and Projected Unit Credit (PUC) methods. The simulation was carried out at the age of 20 to 48 years and groups I to XVII. This calculation follows the 100% one-time pension benefit for a service period of 10 to 15 years and 20% at once for a service period of more than 15 years, with a normal retirement age of 58 years. The results of the study show that the EAN method produces constant normal contributions, while the PUC method produces contributions that increase every year, the normal monthly contributions increase monotonically based on the group and age of entry into work until retirement. In addition, the EAN method produces greater lumpsum benefits than the PUC method. The 17 PPPK groups take into account the projected pension fund present value future benefits, normal contributions, actuarial liabilities, and lumpsum benefits that are more realistic and sustainable.
subject: Articles
  topic: section
subject: Pension Funds
  topic: keywords
subject: Entry Age Normal
  topic: keywords
subject: Government Employees with Employment Agreements
  topic: keywords
subject: Projected Unit Credit
  topic: keywords
subject: Lumpsum Benefit
  topic: keywords
creator: Khalil Rafif
creator: Illuminata Wynnie
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 052
ending page: 068
doi: 10.65689/iajvol2no1pp052-068

Robust E-Bayesian Estimation and Prediction of Esscher Premium for Car Insurance Claim Frequencies Under a Negative Binomial Model
type: item
description: Car insurance claim frequencies often exhibit overdispersion, making the Poisson model too restrictive for premium estimation. This study develops a Negative Binomial-based Bayesian and E-Bayesian framework for estimating and predicting Esscher premiums using aggregated car insurance claim-frequency data. The novelty of this study lies in combining a closed-form Esscher premium under the Negative Binomial model with Bayesian conjugate updating and E-Bayesian hyperparameter averaging to reduce sensitivity to prior specification. A simulated aggregated claim-frequency table with 1,200 exposure units was used to illustrate the proposed framework. The data contained 642 total claims, with an empirical mean of 0.5350 and a sample variance of 0.8378. The variance-to-mean ratio of 1.5660 confirmed overdispersion and supported the use of the Negative Binomial model over the Poisson model. The method-of-moments estimates were for the dispersion parameter and for the success probability. At the representative tilt parameter , the Esscher premiums obtained from the method-of-moments, Bayesian, and E-Bayesian approaches ranged from 0.9004869 to 0.9059240, indicating stable premium estimates across alternative estimation methods. The sensitivity analysis showed that the Esscher premium increases nonlinearly with the tilt parameter, confirming its role as a risk-loading control. The prequential illustration further showed that the framework can support one-step-ahead prediction for aggregated claim totals. Overall, the proposed approach provides a robust and analytically tractable premium estimation framework for overdispersed car insurance claim-frequency data when prior information is uncertain and only aggregated data are available.
subject: Articles
  topic: section
creator: Eli Zulkatri
creator: Muhammad Azka
creator: Ahmad Fuad Zainuddin
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 069
ending page: 080
doi: 10.65689/iajvol2no1pp069-080

Forecasting and Financial Risk Analysis Using ARIMA Intervention Model: A Case Study on JMAS Tbk
type: item
description: The capital market is characterized by high volatility, making accurate forecasting and risk measurement essential for investment decision-making. This study aims to apply the Autoregressive Integrated Moving Average (ARIMA) intervention model and the Value at Risk (VaR) approach for stock prices forecasting and finansial risk analysis.The data consist of monthly stock prices of PT Asuransi Jiwa Syariah Jasa Mitra Abadi Tbk (JMAS) from January 2018 to December 2025. The ARIMA intervention model is applied to identify and quantify structural changes caused by external shocks, particularly the COVID-19 pandemic. The results indicate that the ARIMA (1,2,0) intervention model is the most appropriate model, with a step intervention function reflecting a sudden and permanent impact on stock price movements. The model satisfies diagnostic assumptions and demonstrates good forecasting accuracy, with a Mean Absolute Percentage Error (MAPE) of 13.01%. Forecasting results for January to March 2026 show that stock prices are expected to remain relatively low, indicating a slow post-pandemic recovery. Financial risk is measured using the Cornish-Fisher Value at Risk (VaR) approach at a 95% confidence level. The estimated VaR is -0.4245 indicating a maximum potential loss of 42.45% over a one-month period. This high level of risk reflects extreme market conditions during the COVID-19 period, which significantly increased volatility. This study contributes to financial analysis by integrating intervention-based time series modeling with risk measurement in a unified framework.
subject: Articles
  topic: section
subject: ARIMA Intervention
  topic: keywords
subject: Forecasting
  topic: keywords
subject: Stock Price
  topic: keywords
subject: Value at Risk
  topic: keywords
subject: Volatility
  topic: keywords
creator: Rina Yuliantika
creator: Indah Gumala Andirasdini
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 013
ending page: 023
doi: 10.65689/iajvol2no1pp013-023

Estimation of Ruin Probabilities in an Extended Risk Model with Inhomogeneous Claim Counts and Financial Risks
type: item
description: 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.
subject: Articles
  topic: section
subject: Ruin Probability
  topic: keywords
subject: Inhomogeneous Poisson Process
  topic: keywords
subject: Financial Risk
  topic: keywords
subject: Subexponential Claims
  topic: keywords
subject: Proportional Taxation
  topic: keywords
creator: Nyanumba Walter Motanya
creator: Oduar D. Brian
creator: Joseph O. Nyakinda
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 040
ending page: 051
doi: 10.65689/iajvol2no1pp040-051

Portfolio Optimization and Risk Estimation of LQ45 Mining Stock Using The ARIMA-GARCH-EVT-COPULA Hybrid Model as Alternative Pension Fund Investment
type: item
description: 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 dependenc…
subject: Articles
  topic: section
subject: ARIMA-GARCH
  topic: keywords
subject: Copula
  topic: keywords
subject: Extreme Value Theory
  topic: keywords
subject: Risk
  topic: keywords
subject: Pension Fund
  topic: keywords
creator: Dyah Ayu Mahanani
creator: Galuh Oktavia Siswono
creator: Ulil Azmi
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 096
ending page: 111
doi: 10.65689/iajvol2no1pp096-111

Measuring Risk Aversion Behavior Using Szpiros Approach: Case Study in Indonesias Life Insurance Industry
type: item
description: 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.
subject: Articles
  topic: section
subject: Demand
  topic: keywords
subject: Life Insurance
  topic: keywords
subject: Risk Aversion
  topic: keywords
subject: Szpiro’s Approach
  topic: keywords
creator: Kristio Rapi
creator: Dominicus Savio Priyarsono
creator: Siti Jahroh
creator: Toni Bakhtiar
rights: Copyright (c) 2026 Indonesian Actuarial Journal
date: 2026-07-31
publication date: 2026-07-31
starting page: 001
ending page: 012
doi: 10.65689/iajvol2no1pp001-012

Comparison of Estimation Methods for the Weibull Distribution in Indonesian Life Tables
type: item
description: 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.
subject: Articles
  topic: section
subject: Indonesian life tables
  topic: keywords
subject: maximum likelihood estimation
  topic: keywords
subject: nonlinear least squares
  topic: keywords
subject: ordinary least squares
  topic: keywords
subject: Weibull distribution
  topic: keywords
creator: Terra Dei Alibazah
creator: Agung Prabowo
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 185
ending page: 202
doi: 10.65689/iajvol01no2pp185-202

Investment-Risk Protection Rider for Unit-Linked Insurance
type: item
description: 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.
subject: Articles
  topic: section
subject: Financial services
  topic: keywords
subject: Unit-Linked Insurance
  topic: keywords
subject: Insurance Rider
  topic: keywords
subject: Derivative Options
  topic: keywords
subject: Dynamic Hedging
  topic: keywords
subject: Investment-Risk Protection
  topic: keywords
creator: Kenneth Gunawan
creator: Helena Margaretha
creator: Yoseph Wastu Winayaka
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 175
ending page: 184
doi: 10.65689/iajvol01no2pp175-184

A Deeper Look Into an Insurance Risk Model with Two Types of Claims and FGM Copula Dependency
type: item
description: 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.
subject: Articles
  topic: section
subject: Ruin probability
  topic: keywords
subject: Farlie-Gumbel-Morgenstern copula
  topic: keywords
subject: Risk model
  topic: keywords
subject: Two types of claims
  topic: keywords
subject: Lundberg’s equation
  topic: keywords
creator: Sandy Salomo Saruan
creator: Adhitya Ronnie Effendie
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 95
ending page: 112
doi: 10.65689/iajvol01no2pp095-112

Analysis of JIBOR Discontinuity: Comparison of Spread Adjustment for Several Alternative Reference Rates for 1-Month JIBOR
type: item
description: 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
subject: Articles
  topic: section
subject: JIBOR Transition
  topic: keywords
subject: Alternative Reference Rate
  topic: keywords
subject: Spread Adjustment
  topic: keywords
subject: JIBOR Forecasting
  topic: keywords
creator: Harly Zulfikar
creator: Afif Amrullah Taufiq
creator: Among Giyatno
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 164
ending page: 174
doi: 10.65689/iajvol01no2pp164-174

Modelling The Probability of Insurance Company’s Bankruptcy Using Integro-Differential Equation and Its Simulation
type: item
description: 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.
subject: Articles
  topic: section
subject: insurance
  topic: keywords
subject: surplus process
  topic: keywords
subject: ruin probability
  topic: keywords
subject: integro-differential equation
  topic: keywords
subject: linear combination distribution of two exponential distributions
  topic: keywords
creator: Ghafira Nur Maulida
creator: Agung Prabowo
creator: Supriyanto Supriyanto
creator: Mustafa Mamat
creator: Sukono Sukono
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 84
ending page: 94
doi: 10.65689/iajvol01no1pp084-094

Application Of Annual Ratchet Method And Black-Scholes Model In The Calculation Of Single Net Premium Of Unit-Linked Endowment Life Insurance
type: item
description: 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.
subject: Articles
  topic: section
subject: Premiums
  topic: keywords
subject: Life Insurance
  topic: keywords
subject: Benefit Minimum
  topic: keywords
subject: Unit-Linked
  topic: keywords
subject: Life Insurance Premium
  topic: keywords
subject: Annual Ratchet
  topic: keywords
subject: Black Scholes
  topic: keywords
creator: Husnul Fausiah Magistrawati
creator: Ainun Mawaddah Abdal
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 20
ending page: 32
doi: 10.65689/iajvol01no1pp020-032

Identifying Weakly Correlated Dominating Stocks using Maximum Independent Set
type: item
description: 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.
subject: Articles
  topic: section
subject: Portfolio Optimization
  topic: keywords
subject: Stocks
  topic: keywords
subject: Investment
  topic: keywords
subject: Maximum Independent Set
  topic: keywords
creator: Yeremia Bertolla Gimanjar
creator: Diah Prastiwi
creator: Fendy Septyanto
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 128
ending page: 136
doi: 10.65689/iajvol01no2pp128-136

Cost Component Calculation for Endowment Insurance Premiums on Multiple Life Using the Gompertz Distribution
type: item
description: 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.
subject: Articles
  topic: section
subject: Gross premium
  topic: keywords
subject: Endowment Life Insurance
  topic: keywords
subject: Multiple Life
  topic: keywords
subject: Gompertz Distribution
  topic: keywords
subject: Linear Regression
  topic: keywords
subject: Bounded Optimization
  topic: keywords
creator: Ady Febrisutisyanto
creator: Dwi Haryanto
creator: Antonia Samantha Damara
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 152
ending page: 163
doi: 10.65689/iajvol01no2pp152-163

Development of Economic Capital Using Value-at-Risk (VaR) for Catastrophe (Re)Insurance
type: item
description: 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.
subject: Articles
  topic: section
subject: risk quantification
  topic: keywords
subject: economic capital
  topic: keywords
subject: value at risk
  topic: keywords
subject: catastrophe modelling
  topic: keywords
subject: stress scenarios
  topic: keywords
creator: Danar Handoyo -
creator: Rahmalia Falah Anwar -
creator: Ruben Damanik
creator: Rico Fernando Nainggolan
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 46
ending page: 59
doi: 10.65689/iajvol01no1pp046-059

Forecasting Rupiah-to-US Dollar Exchange Rate 2020 - 2025 Using a Fuzzy Time Series Markov Chain Model
type: item
description: 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.
subject: Articles
  topic: section
subject: exchange rate
  topic: keywords
subject: forecasting
  topic: keywords
subject: fuzzy time series
  topic: keywords
subject: hybrid model
  topic: keywords
subject: markov chain
  topic: keywords
creator: Tiur Masayu Rahmadani
creator: Rosa Maeni
creator: Camelia Miftahur Rizki Kiem Hwa
creator: Iftha Nikmatul Khasanah
creator: Winner Yeo
creator: Kgs. M. Rifat Alfarisi
creator: Yohana Joevanca Kurniawan
creator: Adriano Fadlan Juwono
creator: Mey Lista Tauryawati
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 60
ending page: 72
doi: 10.65689/iajvol01no1pp060-072

Catastrophe Reinsurance Single Premium Valuation Model Based on Indonesia's Earthquake Data
type: item
description: 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 assump…
subject: Articles
  topic: section
subject: Catastrophe Reinsurance
  topic: keywords
subject: Extreme Losses
  topic: keywords
subject: Peaks Over Threshold
  topic: keywords
subject: Copula
  topic: keywords
subject: Monte Carlo
  topic: keywords
creator: Priscilla Natalie Nurtanio
creator: Pieter Realino
creator: Temmy Sugiarto
creator: Darren Nathaniel
creator: Raymond Tjandra
creator: Theresa Angelina
creator: Arzu Nafiputra
creator: Dave Filbert Iglesias Lukman
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 113
ending page: 127
doi: 10.65689/iajvol01no2pp113-127

Precision-Oriented Churn Prediction with a Fine-Tuned Meta-Learner Stack Model and SHAP: A Case Study on IBM Telco
type: item
description: 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.
subject: Articles
  topic: section
subject: churn
  topic: keywords
subject: model
  topic: keywords
subject: stacking
  topic: keywords
subject: SHAP
  topic: keywords
subject: analysis
  topic: keywords
creator: Tajmahal Ghaza Antani
creator: Adhan Haidar Hakim
creator: Rayna Nurrizky
creator: Venny Annelia Einstania Vyorra
creator: Fendy Septyanto
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-12-31
publication date: 2025-12-31
starting page: 137
ending page: 151
doi: 10.65689/iajvol01no2pp137-151

Valuation of Pension Funds with Attained Age Normal and Projected Unit Credit Methods: Case Study of PT Taspen (Persero) Samarinda Branch
type: item
description: 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.
subject: Articles
  topic: section
subject: Pension Fund
  topic: keywords
subject: Attained Age Normal
  topic: keywords
subject: Project Unit Credit
  topic: keywords
subject: PT Taspen (Persero) Samarinda
  topic: keywords
creator: Annisa Nur Auliya
creator: Indrawan Indrawan
creator: Muhammad Azka
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 33
ending page: 45
doi: 10.65689/iajvol01no1pp033-045

Advancing Sharia Insurance Product for Natural Disaster Risks: A Collective Risk Model Approach
type: item
description: 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.
subject: Articles
  topic: section
subject: CRM
  topic: keywords
subject: natural disaster
  topic: keywords
subject: sharia insurance
  topic: keywords
creator: Trecy Elisabet Tioralina Saragih
creator: Alfonsius Lintang
creator: Chintya Luminar Sinaga
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 9
ending page: 19
doi: 10.65689/iajvol01no1pp009-019

Use of Actuarial Models for Determining Premiums and Reserves
type: item
description: 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.
subject: Articles
  topic: section
subject: crucial aspects
  topic: keywords
subject: exploration
  topic: keywords
subject: monte carlo
  topic: keywords
subject: premium
  topic: keywords
subject: reserves
  topic: keywords
creator: Soehardjoepri Soehardjoepri
creator: Rahmania Azwarini
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 73
ending page: 83
doi: 10.65689/iajvol01no1pp073-083

Analysis of the Health Social Security Administration (BPJS Kesehatan) Claim Amount using Random Forest Regression
type: item
description: 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.
subject: Articles
  topic: section
subject: BPJS Kesehatan
  topic: keywords
subject: machine learning
  topic: keywords
subject: random forest regression
  topic: keywords
subject: claim amount
  topic: keywords
creator: Indah Gumala Andirasdini
creator: Desta Saputra
creator: Muklas Rivai
creator: Septia Eka Marsha Putra
rights: Copyright (c) 2025 Indonesian Actuarial Journal
date: 2025-08-05
publication date: 2025-08-05
starting page: 1
ending page: 8
doi: 10.65689/iajvol01no1pp001-008