•Various ML & XAi methods used for medical insurance cost prediction were reviewed.•Random Forest, GBM, and XGBoost methods were deployed and compared in this study.•SHAP analysis and ICE plots XAi ...methods were deployed and compared in this study.•The XAi methods was used to identify the key insurance premium price determinants.•This study is a good decision-support system for stakeholders in Medical insurance.
Predictive modeling in healthcare continues to be an active actuarial research topic as more insurance companies aim to maximize the potential of Machine Learning (ML) approaches to increase their productivity and efficiency. In this paper, the authors deployed three regression-based ensemble ML models that combine variations of decision trees through Extreme Gradient Boosting (XGBoost), Gradient-boosting Machine (GBM), and Random Forest (RF) methods in predicting medical insurance costs. Explainable Artificial Intelligence (XAi) methods SHapley Additive exPlanations (SHAP) and Individual Conditional Expectation (ICE) plots were deployed to discover and explain the key determinant factors that influence medical insurance premium prices in the dataset. The dataset used comprised 986 records and is publicly available in the KAGGLE repository. The models were evaluated using four performance evaluation metrics, including R-squared (R2), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). The results show that all models produced impressive outcomes; however, the XGBoost model achieved a better overall performance although it also expanded more computational resources, while the RF model recorded a lesser prediction error and consumed far fewer computing resources than the XGBoost model. Furthermore, we compared the outcome of both XAi methods in identifying the key determinant features that influenced the PremiumPrices for each model and whereas both XAi methods produced similar outcomes, we found that the ICE plots showed in more detail the interactions between each variable than the SHAP analysis which seemed to be more high-level. It is the aim of the authors that the contributions of this study will help policymakers, insurers, and potential medical insurance buyers in their decision-making process for selecting the right policies that meet their specific needs.
This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that ...may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus.
In this study, we examine the feasibility of reverse mortgages in Brazil from the perspectives of both policyholders and insurers. Reverse mortgage is a financial product where the property's ...ownership is transferred to an insurance company in exchange for a guaranteed annuity, while the insured retains the right to use such property until their death. Using monthly real state pricing data (2008–2019) provided by FipeZAP, we employ statistical modeling to predict future prices of properties to get the future insurer's expected results, while policyholders' annuity benefits are calculated using actuarial approach. To assess attractiveness, we calculate internal rate of return for different policyholder profiles and conduct profit test for the insurer. Our results indicate that, as an investment strategy, reverse mortgage has little or no attractiveness to the policyholder despite its actuarial fairness. However, it may be a viable option for increasing retirement income in case of a consistent real estate overvaluation. For insurers, the results are unfeasible due to the extended time lag for positive financial results, which only occurs after the policyholder's death. The inclusion of safety loadings can produce more favorable outcomes. Nonetheless, we recommend incorporating reverse mortgages as an elderly policy strategy to reduce reliance on state support during retirement, even if no attractive returns are provided as a financial investment. We also discuss policy implications (e.g., right to the city) to help the elderly stay connected to social support networks and local services.
•We evaluate the feasibility of Reverse Mortgages in Brazil.•We forecast future house prices and use actuarial approach to calculate benefits.•Results show little attractiveness as financial investments for most risk profiles.•Insurers may face unfeasible outcomes, but loadings can produce favorable outcomes.•Reverse mortgages can contribute to improving the right to the city for the elderly.
The method of actuarial modeling is applied in pension or social insuranceschemes. However, the possibilities of using this method also occur in non-life .insurance,which includes health insurance. ...The aim of the paper is to point out the application ofactuarial modeling to determine the rate of compulsory health insurance in the solidarityhealth system. For this reason, in the paper we use Slovak Health System based onBismarck model as a case study for application of the chosen method. In the case study weuse a PESTLE analysis for better understanding of current situation. The paper usessecondary data collected in the period 2009 - 2019 from the official documents of Ministryof Health of the Slovak Republic. Based on actuarial modeling we determine the rate ofhealth insurance for the economically inactive population at 6.3 % of the assessment base.This is a change of 2.3 points compared to the current official rate and 9.03 points increasein the state's share in the creation of resources from compulsory health insurance. Thepaper has an application character. Therefore, we conclude that the method of actuarialmodeling can be used to determine the rate in the solidary health care systems.
In insurance industry, the financial stability of insurance companies represents an issue of vital importance. In order to maintain the financial stability and meet minimum regulatory requirements, ...actuaries apply actuarial modeling. Modeling has been at the center of actuarial science and of all the sciences from the beginning of their journey. In insurance industry, actuarial modeling creates a framework that allows actuaries to identify, understand, quantify and manage a wide range of risks, especially actuarial risks. Actuarial modeling uses as key instruments actuarial models which represent a simplification of a real system, facilitating understanding and prediction of the real system. Therefore, these models are designed to be appropriate with the essential principles of actuarial science. In actuarial modeling progress is marked by breaking existent barriers and developing and incorporating new types of actuarial models.
Surrender and paid-up states are incorporated in the valuation of guaranteed benefits and payments of a level premium paying life insurance policy.
We present different valuation methods and examine ...to what extent they avoid capitalizing and releasing future loadings which are associated with the payment of future premiums.
We demonstrate how to avoid capital being required in the future to cover valuation strains. The paid-up benefit valuation method is being extended so that it does not require the premium basis to be on the safe-side of the valuation basis. We obtain a unification and integration of the level premium and paid-up valuation principles.
An actuarial model is developed to reveal the intrinsic nature of participating life insurance. The basic safe-side criterion is examined. It is established how the first-order prospective net ...premium reserve includes safety margins or bonus loadings, and it is demonstrated how the bonus loadings are currently released. It is demonstrated how surplus may be distributed and accumulated as a terminal bonus in an equitable way. The level premium is divided into a variable recurrent single premium and a variable natural premium, and an alternative to the prospective net premium reserve is examined. A capitalization of future safety margins or bonus loadings, which are related to past premiums and the paid-up benefit, may allow the insurance company a considerable increase in investment freedom. The theory is illustrated by numerical results.
In an insurance context, Long-Term Care (LTC) products cover the risk of permanent loss of autonomy, which is defined by the impossibility or difficulty of performing alone all or part of the ...activities of daily living (ADL). From an actuarial point of view, knowledge of risk depends on knowledge of the underlying biometric laws, including the mortality of autonomous insureds and the mortality of disabled insureds. Due to the relatively short history of LTC products and the age limit imposed at underwriting, insurers lack information at advanced ages. This represents a challenge for actuaries, making it difficult to estimate those biometric laws. In this paper, we propose to complete the missing information at advanced ages on the mortality of autonomous and disabled insured populations using information on the global mortality of the portfolio. In fact, the three previous mortality laws are linked since the portfolio is composed only of autonomous and disabled policyholders. We model the two mortality laws (deaths in autonomy and deaths in LTC) in a Poisson Generalized Linear Model framework, additionally using the P-Splines smoothing method. A constraint is then included to link the mortality laws of the two groups and the global mortality of the portfolio. This new method allows for estimating and extrapolating both mortality laws simultaneously in a consistent manner.
