IFoA SA3 cheat sheet

General Insurance (SA3)

• Pure premium = expected frequency × expected severity; load for expenses, profit, and risk margin to get gross premium.

• Chain-ladder development factor: f_j = Σ C_{i,j+1} / Σ C_{i,j} across accident years i with data at both development periods j and j+1.

• Bornhuetter-Ferguson ultimate = reported to date + (expected ultimate × (1 − % reported)); expected ultimate = exposure × a priori loss ratio.

• Mack's chain-ladder standard error: process variance plus parameter variance; the process variance component uses σ²_j estimated from weighted residuals.

• Over-dispersed Poisson (ODP) bootstrap: resample Pearson residuals, refit GLM, derive predictive distribution of reserves; captures both process and parameter uncertainty.

• Solvency II SCR for non-life premium and reserve risk: SCR = 3 × σ × V, where V = (V_prem + V_res) and σ combines premium and reserve coefficients by volume-weighted average.

• Reinsurance decision rule: cede when the marginal reduction in cost of capital plus expected recoveries exceeds the reinsurance premium loading.

• IBNR = ultimate loss − reported (case) reserves; IBNER is the development on known claims, often separated from pure IBNR for very late-reported classes.