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

TL;DR

This paper applies functional data analysis to loss development patterns in P&C insurance, introducing a probabilistic forecasting model that outperforms traditional methods in accuracy and uncertainty quantification.

Contribution

It develops a novel functional model for ILR curve completion and uncertainty quantification, leveraging PCA, partial least squares, and bootstrapping techniques.

Findings

The proposed method yields superior probabilistic scores compared to Chain Ladder.

It provides accurate functional predictive intervals for ILR curves.

The analysis identifies key covariates influencing development patterns.

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.