A table crossing accident years with the development of payments, the basis for projecting ultimate losses and for reserving.
The loss development triangle is the fundamental tool of non-life reserving. It takes the form of a table crossing, in rows, the accident years in which losses occur and, in columns, the development years, that is, the time elapsed since occurrence, each cell showing the cumulative amount paid or estimated at that stage. Its triangular shape arises because recent losses have only a little observed development, whereas older ones are almost fully run off. The challenge is precisely to complete the triangle, projecting the future development of recent years from the patterns observed in older ones. The best-known method, the chain ladder, computes factors for moving from one development year to the next and applies them to estimate the ultimate burden of each cohort, from which the reserves to be set are derived. Simple and robust for mature, stable lines, this approach shows its limits for emerging risks such as cyber, where the track record is short, development patterns are unstable and the threat is evolving, which makes the computed factors unreliable and calls for judgemental adjustments.
An actuary observes, from the triangles, that a line's losses are 90 percent paid after three years. They apply this pattern to recent cohorts to estimate their ultimate burden, but for cyber the instability of the triangles forces them to supplement this mechanism with expert judgment.
triangle de liquidation, chain ladder, méthode de la chaîne, loss triangle