Symbol Definition
\[Y\] Total number of accident years in the triangle
\[D\] Total number of development ages, in years. Usually, \(D = Y\)
\[U_{y,\ d}\] Estimated ultimate loss in accident year \(y\) evaluated at development age \(d\)
\[C_{y,\ d}\] Paid or incurred claims in accident \(y\) evaluated at development age \(d\)
\[g_{d}\] Random variable denoting the age-to-age ultimate development factor applicable for ultimate losses from age \(d\) to \(d + 1\).
\[g_{y,\ \ d}\] Age-to-age ultimate development factor for accident year \(y\) from age \(d\) to \(d + 1\). Note that \(g_{y,d} = U_{y,\ d + 1}/U_{y,\ d}\). (Eq 3.03)
\[G_{d}\] Random variable denoting the age-to-ultimate ultimate development factor applicable for ultimate losses from age \(d\) to maturity age \(D\). Note that \(G_{d} = \prod_{i = d}^{D}g_{i}\).
\[r_{y}\] Weight of the estimated ultimate losses in the \(y\)-th accident year as a proportion of the sum of ultimate losses in all available accident years. Note that \(r_{y} ≔ U_{y,D - y + 1}/\sum_{j = 1}^{Y}U_{j,\ D - j + 1\ }\).
\[R_{d}\] Cumulative weight up to development age \(d\), defined as \(R_{d} ≔ \sum_{j = Y - d + 1}^{Y}{r_{j}\ }\).