Aggregate Loss Modeling for Renewal Gross Premium Estimation in Group Health Insurance
Using Zero-Inflated Poisson-Lindley and Mixture Gamma-Rayleigh Distribution
Abstract View: 43,
DOI:
https://doi.org/10.32665/statkom.v5i1.6426Keywords:
Group health insurance, Medical Inflation, Zero-Inflated Poisson-Lindley, , Mixture Gamma-Rayleigh Distribution, Gross PremiumAbstract
Background: Group health insurance policy renewals require insurers to re-evaluate premiums based on historical claim experience. Medical inflation heightens uncertainty by driving up future healthcare costs.
Objective: This study estimates the renewal gross premium for a group health insurance portfolio using an aggregate loss risk modeling approach.
Methods: Historical claim data covered 912 insured individuals, with 102 claimants and 174 claims recorded between July 2024 and June 2025, drawn from a corporate client of an Indonesian insurance company. Claim frequency was modeled using the Zero-Inflated Poisson–Lindley (ZIPL) distribution to handle excess zeros and overdispersion, while claim severity was modeled with the Mixture Gamma–Rayleigh Distribution (MGRD) to capture medical cost heterogeneity. Parameters were estimated via Maximum Likelihood Estimation, and a 95% confidence interval for expected severity was derived using Chebyshev's inequality. The model assumes a 16.2% medical inflation rate, a 6.5% annual interest rate, and an 18% loading factor.
Results: At a 95% confidence level, the estimated renewal gross premium ranges from IDR 2.053 billion to IDR 4.352 billion. Sensitivity analysis confirms that premiums rise with increasing medical inflation.
Conclusion: The interval-based approach provides a statistically grounded numerical basis for underwriting decisions and negotiations in group health insurance renewals.
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