9.2 Notations

Definition 9.1 Same notations as Venter for \(n \times n\) triangle

  • \(w\): Accident (exposure) year

  • \(d\): Development age

  • \(q(w,d)\): incremental loss for AY \(w\) from age \(d-1\) to \(d\)

  • \(c(w,d)\): cumulative loss

  • \(F(d)\): Incremental LDF from age \(d\) to \(d+1\)

  • \(f(d)\): \(F(d) - 1\), for forcasting incremental losses

  • \(G(w)\): Factor relating to accdient (exposure) year \(w\); ultimate gross level

  • \(h(k)\): Factor relating to the diagonal \(k\) along which \(w+d\) is constant

Table 9.1: Incremental triangle with corresponding row and column parameters
- \(\beta_2\) \(\beta_3\)
\(\alpha_1\) \(q(1,1)\) \(q(1,2)\) \(q(1,3)\)
\(\alpha_2\) \(q(2,1)\) \(q(2,2)\)
\(\alpha_3\) \(q(3,1)\)

Chainladder assumptions:

  1. LDFs are the same for each row

    \(F(w,d) = F(d)\)

  2. Each AY has a parameter representing it’s level

    e.g. CL project based on level of losses to date