Functional Analysis of Loss-development Patterns in P&C Insurance

2025-10-31

AI Summary

This study addresses loss development modeling for workers’ compensation insurance in North America. Using incremental loss ratio (ILR) curves from 24 accident years and over 3,300 lines of business in the NAIC Schedule P dataset, we propose a functional probabilistic forecasting framework. Methodologically, the approach integrates functional data depth to detect anomalous ILR patterns, combines functional principal component analysis with partial least squares regression to build company-level covariate-driven predictive models, and employs functional bootstrapping to jointly quantify uncertainty across all development lags. Compared to the classical chain-ladder method, our framework achieves significantly improved probabilistic forecast accuracy, yields well-calibrated functional prediction intervals, and provides robust support for loss reserve estimation and risk-informed decision-making.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We analyze loss development in NAIC Schedule P loss triangles using functional data analysis methods. Adopting the functional viewpoint, our dataset comprises 3300+ curves of incremental loss ratios (ILR) of workers' compensation lines over 24 accident years. Relying on functional data depth, we first study similarities and differences in development patterns based on company-specific covariates, as well as identify anomalous ILR curves. The exploratory findings motivate the probabilistic forecasting framework developed in the second half of the paper. We propose a functional model to complete partially developed ILR curves based on partial least squares regression of PCA scores. Coupling the above with functional bootstrapping allows us to quantify future ILR uncertainty jointly across all future lags. We demonstrate that our method has much better probabilistic scores relative to Chain Ladder and in particular can provide accurate functional predictive intervals.

Problem

• Analyzing loss development patterns in property casualty insurance data
• Identifying anomalous loss development curves using functional data analysis
• Developing probabilistic forecasting models for incomplete loss development curves

Innovation

• Functional data analysis of loss development patterns
• Partial least squares regression of PCA scores
• Functional bootstrapping for uncertainty quantification