Risk aggregation in non-life insurance: Standard models vs. internal models

Standard models for capital requirements restrict the correlation between different risk factors to the linear measure and do not consider undertaking-specific parameters. We propose a comprehensive framework for risk aggregation in non-life insurance using copulas and two levels of aggregation: base-level aggregation (different assets, different lines of insurance) and top-level aggregation (assets and liabilities). Using empirical data from Korean and German insurance companies, we compare our internal risk model with three regulatory standard models (Korean RBC, Solvency II, Swiss Solvency Test). We show that the standard models significantly overestimate the potential risk size for the insurers considered in this study by 61.2% and 57.8% on average for the Korean and the German cases respectively, where almost half of the overestimation level results from the uniform risk profile imposed by regulations and the other half comes from the linear correlation assumption. The differences between standard models and internal models might distort competition when both approaches are used in one market.