Tail Models

For all tail models, we use \(\mathcal{Y}\) to denote the loss development triangle for an aggregated pool of insurance policies, defined by:

\[\mathcal{Y} = \{y_{ij} : i = 1, ..., N; j = 1, ..., N - i + 1\}\]

where \(y_{ij}\) is the cumulative loss amount for accident year \(i\) at development lag \(j\). In real-world data, losses for a given accident year \(i\) are only known up to development lag \(j = N - i + 1\), creating the triangular data structure that loss triangles are named for. However, sometimes historic data will be available such that we have a full square, in which case we indicate the development lag with \(j = 1, ..., M\).

Note that most of our tail models use loss ratios as the target variable as opposed to cumulative losses. In such cases we use \(\mathcal{LR}\) to denote loss ratios, where \(LR_{ij} = y_{ij} / EP_{i}\) and \(EP_{i}\) indicates the total earned premium for the given accident period. In either case, predictions are always generated and returned to the user on the loss scale.

Available Models

• Generalized Bondy Model (GeneralizedBondy)
  • Model Fit Configuration
  • Model Predict Configuration
• Sherman Model (Sherman)
  • Model Fit Configuration
  • Model Predict Configuration
• Classical Power Transform
  • Model Fit Configuration
  • Model Predict Configuration