Qiheng (Steve) Guo's Abstract
Loss development, in terms of loss development factors (LDF) and incremental
loss ratio (ILR) in P&C insurers’ business lines, can be viewed as functional
data across development period and has discrete observations in NAIC Schedule
P loss triangles. Regulators, reinsurers and other parties’ may wish to learn from
a large number of triangles to find out patterns and anomalies of loss development
in the market. Relying on robust principal component analysis (RPCA), we study workers’ compensation line across hundreds of companies and over ten years. RPCA can be applied to functional data and helps us to (i) detect and isolate outlying loss development; (ii) reduce the dimension of functional data to three dimensions that can be interpreted to short-term, mid-term and long-term loss development. Our analysis shows that companies in different regions and with different business focus tend to have separate development patterns. As a key contribution, our findings provide a more profound understanding of loss development in the market as well as easy-to-use analysis and visualization tools. A more advanced technique based on robust tensor PCA is also discussed.