Article 245: Machine Learning Elastic Net Regression in R for Actuarial Science: End-to-End Case Studies

This article demonstrates how Elastic Net Regression can be applied in actuarial science using R to manage multicollinearity, improve predictive accuracy, and deliver interpretable insights across life, health, and general insurance applications.

Article Outline

1. Introduction to Elastic Net Regression in Actuarial Science

• Importance of regression models in actuarial science for pricing, reserving, mortality forecasting, and claims analysis.

• The challenge of multicollinearity among actuarial predictors (e.g., age, tenure, exposure, lifestyle factors).

• Why Elastic Net, combining Ridge and Lasso penalties, provides a balanced approach for actuarial applications.

2. Applications of Elastic Net in Actuarial Science

• Life Insurance: modeling mortality risk with demographic and lifestyle variables.

• Health Insurance: predicting medical claim severity using policyholder characteristics.

• General Insurance: estimating claim frequency and severity from driver, vehicle, and exposure attributes.

• Pension and Retirement Modeling: forecasting annuity payouts using correlated demographic and economic variables.

3. Mathematical Foundation of Elastic Net Regression

• Elastic Net objective function: residual sum of squares + λ(α × L1 penalty + (1–α) × L2 penalty).

• Explanation of hyperparameters:

  • λ (lambda): overall strength of regularization.

  • α (alpha): balance between Ridge (0) and Lasso (1).

• Why this hybrid penalty is well-suited to actuarial datasets with overlapping explanatory factors.

4. Setting Up the R Environment

• Required R packages: glmnet, caret, dplyr, ggplot2.

• Notes on reproducibility and cross-validation.

5. Creating Actuarial Datasets (Simulated for Case Studies)

• Case Study 1 (Life Insurance Mortality Risk): mortality risk modeled by age, BMI, smoker status, and medical history.

• Case Study 2 (Health Insurance Claim Severity): claim costs modeled from demographics, chronic conditions, and utilization.

• Case Study 3 (Motor Insurance Claim Frequency): claim frequency modeled by driver age, vehicle age, mileage, and risk indicators.

6. Preprocessing Actuarial Data

• Train-test splitting with caret::createDataPartition.

• Scaling and standardizing predictors.

• Handling categorical actuarial factors (e.g., smoker, risk indicator).

7. Building Elastic Net Models in R

• Using cv.glmnet for cross-validation to select λ.

• Tuning α across a grid.

• Interpreting coefficients in actuarial terms.

8. Case Study 1: Life Insurance Mortality Risk

• Fitting Elastic Net and evaluating performance with R² and RMSE.

• Interpreting coefficients such as age, smoker status, and medical history.

9. Case Study 2: Health Insurance Claim Severity

• Training and evaluating the model.

• Coefficient interpretation for age, comorbidities, utilization, and policy duration.

10. Case Study 3: Motor Insurance Claim Frequency

• Applying Elastic Net to driver and vehicle features.

• Model performance and coefficient insights.

11. Comparing Elastic Net with Ridge and Lasso

• Fit Ridge (α = 0), Lasso (α = 1), and Elastic Net (0 < α < 1).

• Compare R² and RMSE across the three case studies.

• Visualize performance differences with bar plots.

12. Advantages and Limitations in Actuarial Applications

• Advantages: stability, interpretability, feature selection, regulatory friendliness.

• Limitations: assumes linearity, requires tuning, sensitive to scaling.

13. End-to-End R Script (All Case Studies)

• Unified script including dataset creation, preprocessing, modeling, evaluation, and comparisons.

14. Conclusion

• Recap of Elastic Net’s role in actuarial science.

• Emphasis on its ability to balance robustness and interpretability.

• Future directions: extensions with GLMs, GLMMs, and survival analysis.

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