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.
Stochastic Multi-State Modeling for Critical Illness Insurance With Integration of Non-Homogeneous Trends and Pandemic Shocks
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.
Copyright (c) 2026 Indonesian Actuarial Journal
Multiple Decrement Modeling of BPJS Health Transitions Under Air Pollution Exposure in DKI Jakarta
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.
Government Employees with Employment Agreements Pension Fund Valuation Across 17 Salary Grades Using Entry Age Normal and Projected Unit Credit
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.
Government Employees with Employment Agreements
Robust E-Bayesian Estimation and Prediction of Esscher Premium for Car Insurance Claim Frequencies Under a Negative Binomial Model
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.
Forecasting and Financial Risk Analysis Using ARIMA Intervention Model: A Case Study on JMAS Tbk
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.
Estimation of Ruin Probabilities in an Extended Risk Model with Inhomogeneous Claim Counts and Financial Risks
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.
Portfolio Optimization and Risk Estimation of LQ45 Mining Stock Using The ARIMA-GARCH-EVT-COPULA Hybrid Model as Alternative Pension Fund Investment
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.
Measuring Risk Aversion Behavior Using Szpiros Approach: Case Study in Indonesias Life Insurance Industry
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.
Comparison of Estimation Methods for the Weibull Distribution in Indonesian Life Tables
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.
Copyright (c) 2025 Indonesian Actuarial Journal
Investment-Risk Protection Rider for Unit-Linked Insurance
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.
A Deeper Look Into an Insurance Risk Model with Two Types of Claims and FGM Copula Dependency
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.
Analysis of JIBOR Discontinuity: Comparison of Spread Adjustment for Several Alternative Reference Rates for 1-Month JIBOR
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
Modelling The Probability of Insurance Company’s Bankruptcy Using Integro-Differential Equation and Its Simulation
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.
linear combination distribution of two exponential distributions
Application Of Annual Ratchet Method And Black-Scholes Model In The Calculation Of Single Net Premium Of Unit-Linked Endowment Life Insurance
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.
Identifying Weakly Correlated Dominating Stocks using Maximum Independent Set
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
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.
Development of Economic Capital Using Value-at-Risk (VaR) for Catastrophe (Re)Insurance
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.
Forecasting Rupiah-to-US Dollar Exchange Rate 2020 - 2025 Using a Fuzzy Time Series Markov Chain Model
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.
Catastrophe Reinsurance Single Premium Valuation Model Based on Indonesia's Earthquake Data
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.
Precision-Oriented Churn Prediction with a Fine-Tuned Meta-Learner Stack Model and SHAP: A Case Study on IBM Telco
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.
Valuation of Pension Funds with Attained Age Normal and Projected Unit Credit Methods: Case Study of PT Taspen (Persero) Samarinda Branch
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.
Advancing Sharia Insurance Product for Natural Disaster Risks: A Collective Risk Model Approach
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.
Use of Actuarial Models for Determining Premiums and Reserves
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.
Analysis of the Health Social Security Administration (BPJS Kesehatan) Claim Amount using Random Forest Regression
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.