Document Type : Original Research Paper

Authors

• Amirmohammad Norouzi ¹
• Mojtaba Ranjbar ²
• Saman Vahabi ³
• Mitra Ghanbarzadeh ⁴

¹ Master Degree, Department of Financial Mathematics and Actuarial, Faculty of Mathematical Sciences, Kharazmi University, Tehran, Iran.

² Associate Professor, Department of Financial Mathematics and Actuarial, Faculty of Mathematical Sciences, Kharazmi University, Tehran, Iran

³ Assistant Professor, Department of Financial Mathematics and Actuarial, Faculty of Mathematical Sciences, Kharazmi University, Tehran, Iran.

⁴ Assistant Professor, Department of Personal Insurance, Insurance Research Center, Tehran, Iran.

Abstract

BACKGROUND AND OBJECTIVES: The conventional approach to life insurance premium pricing relies on standardized mortality tables, which apply uniform survival probabilities to diverse policyholder populations. While this method is computationally straightforward, it overlooks the heterogeneity of individual risk profiles, often resulting in premiums that fail to reflect the true mortality risk of each insured individual. This may lead to pricing inefficiencies, a sense of unfairness among low-risk policyholders and unintended cross-subsidization between high- and low-risk groups where low-risk individuals may overpay to offset losses from higher-risk counterparts. To address these challenges, this study develops a novel framework for constructing personalized mortality tables tailor-made to the unique risk characteristics of each policyholder. By integrating these individualized tables with the Wang premium principle, enhanced by advanced machine learning techniques, the research aims to deliver fairer, more precise, and actuarially sound premium calculations. This approach not only responds to the evolving expectations of modern insurance markets but also supports long-term profitability by retaining low-risk clients through transparent and equitable pricing practices.
METHODS: This study adopts a developmental–applied approach with an analytical design to create risk-adjusted mortality tables reflecting individual policyholder characteristics. Central to the methodology is the development of a composite market risk parameter (λ), which consolidates key risk factors—including age, gender, smoking status, occupation, medical history, contract duration, and death benefit—into a single predictive index. This parameter serves as the cornerstone for the Wang distortion function, a robust mathematical tool that transforms classical survival probabilities into risk-adjusted probabilities, incorporating risk aversion and market dynamics. The estimation of λ leverages historical policyholder data, capturing a comprehensive set of demographic, health, and occupational variables. Two state-of-the-art machine learning algorithms—Random Forest (RF) and Extreme Gradient Boosting (XGBoost)—are deployed to predict λ with high accuracy, capitalizing on their ability to model complex, non-linear relationships among risk factors and handle noisy or heterogeneous data effectively. All data preprocessing, model training, and hyperparameter optimization are conducted using Python, ensuring computational efficiency, scalability, and reproducibility. The predicted λ values are then integrated into the Wang premium principle to compute individualized premium rates, ensuring that pricing reflects the unique risk profile of each policyholder and aligns with actuarial expectations.
FINDINGS: Empirical results underscore the superiority of the proposed framework in delivering equitable and precise premium estimates. By aggregating risk factors into the market risk parameter, the model generates personalized survival probabilities that replace the uniform probabilities of classical mortality tables, offering a more granular and accurate representation of mortality risk. For high-risk policyholders with elevated λ values, premiums calculated using the Wang principle are significantly higher than those derived from traditional methods, ensuring that pricing accurately reflects increased mortality risks. Conversely, low-risk individuals benefit from lower premiums, mitigating the issue of overpricing that often affects this group in conventional frameworks. Feature importance analysis, conducted through the machine learning models, reveals that health-related factors such as medical history and smoking status alongside age, exert the strongest influence on predicting λ, driving significant variability in premium rates. Occupation and gender, while less dominant, contribute meaningfully to risk assessment, highlighting the multidimensional nature of mortality risk modeling. The Random Forest model achieves a mean squared error (MSE) of 0.00028, indicating high predictive accuracy and robustness. These findings demonstrate the framework’s ability to eliminate hidden subsidies between risk groups, ensuring actuarially fair pricing that aligns with individual risk profiles and market realities.
CONCLUSION: The principal contribution of this research lies in its development of a hybrid framework that seamlessly integrates personalized mortality tables with the Wang premium principle, enhanced by machine learning-driven predictions.  By aligning premiums with individual risk profiles, the model ensures actuarial fairness, reduces inefficiencies, and enhances pricing transparency, fostering greater policyholder trust and reducing lapse rates in competitive markets. The findings confirm a consistent pattern: Wang-based premiums exceed classical premiums for high-risk individuals and are lower for low-risk groups, ensuring equitable differentiation across risk profiles. From a practical perspective, insurers adopting this framework can strengthen customer relationships, improve retention of low-risk policyholders, and enhance market competitiveness. Future research could extend this framework to other insurance branches, such as health or property insurance, where personalized risk assessment could yield similar benefits. Incorporating additional data sources, such as behavioral or lifestyle data from wearable devices or financial records, could further refine risk predictions. Exploring hybrid models that combine deep learning with traditional actuarial methods holds promise for enhancing predictive performance, particularly for complex or sparse datasets. A critical next step is validating the model with real-world insurance data, which would provide a robust basis for assessing its practical effectiveness and scalability in diverse market conditions. By modernizing life insurance pricing, this research paves the way for a more equitable, transparent, and customer-centric insurance industry, responding to the growing demand for fairness and precision in pricing practices.




 

Keywords

• Fair pricing
• Life insurance
• Machine learning
• Market price of risk
• Personalized mortality table
• Wang premium

Main Subjects

• Insurance pricing