Reserving Methods Cheat Sheet

Chain Ladder Method

• Age-to-age factor: $f_k = \sum C_{i,k+1} / \sum C_{i,k}$ (weighted average)
• Cumulative development factor: $CDF_k = f_k \cdot f_{k+1} \cdot \ldots \cdot f_{\text{ult}}$
• Ultimate losses: $\text{Ultimate}_i = C_{i,\text{current}} \cdot CDF_{\text{current age}}$
• IBNR: $IBNR_i = \text{Ultimate}_i - \text{Paid}_i$

Bornhuetter-Ferguson Method

• Expected losses: $EL_i = EP_i \cdot ELR$
• Percent unreported: $q_i = 1 - 1/CDF_i$
• BF Ultimate: $\text{Ultimate}_i = \text{Reported}_i + EL_i \cdot q_i$
• BF IBNR: $IBNR_i = EL_i \cdot q_i$

Cape Cod Method

• Used-up premium: $UP_i = EP_i \cdot (1/CDF_i)$
• Expected loss ratio: $ELR = \sum \text{Reported}_i / \sum UP_i$
• Cape Cod Ultimate: $\text{Ultimate}_i = \text{Reported}_i + EP_i \cdot ELR \cdot q_i$

When to Use Each Method

• Chain Ladder: Best when development patterns are stable and historical data is credible
• Bornhuetter-Ferguson: Better for immature accident years with little development data
• Cape Cod: Good compromise when expected loss ratios are uncertain