Rank-based methods for modeling dependence between loss triangles.

Area of Science:

• Actuarial Science
• Statistical Modeling
• Risk Management

Background:

• Property and casualty insurers require accurate multivariate models for loss triangle data to determine aggregate portfolio risk capital.
• The choice of dependence structure significantly impacts reserve estimation accuracy.
• Existing methods may not adequately address the complexities of dependence structures in insurance data.

Purpose of the Study:

• To propose a robust two-stage inference strategy for selecting and validating dependence structures in multivariate loss triangle models.
• To enhance the accuracy of reserve estimation and risk capital determination for insurance portfolios.
• To provide a practical approach for insurers to model dependencies across different lines of business.

Main Methods:

• Fitting generalized linear models (GLMs) to the margins of the loss triangle data.
• Utilizing standardized residuals from GLMs.
• Linking residuals via a copula selected and validated using rank-based methods.
• Applying a two-stage inference strategy for model selection and validation.

Main Results:

• The proposed two-stage strategy effectively assists in model selection and validation for dependence structures.
• Demonstrated application on data from six lines of business of a Canadian insurance company.
• Consideration of two hierarchical dependence models: nested Archimedean copulas and a copula-based risk aggregation model.

Conclusions:

• The two-stage inference strategy offers a reliable method for insurers to choose and validate dependence structures.
• Accurate dependence modeling is crucial for sound reserve estimation and risk capital allocation.
• The approach facilitates better risk management in property and casualty insurance.