Forecasting Models

For all forecasting models, we use \(\mathcal{LR}\) to denote the ultimate loss ratios for an aggregated pool of insurance policies, defined by:

\[\mathcal{LR} = \{LR_{i} : i = 1, ..., N\}\]

where \(LR_{i}\) is the ultimate loss ratio amount for accident period \(i\). In real-world data, ultimate losses for a given accident period \(i\) are only known to the extent that we have sufficient historic data to observe the losses reach their ultimate state. In practice, this means that ultimate loss ratios for recent accident periods will actually be predictions or estimates of the true ultimate loss ratios. In some cases, users may simply assume that the expected ultimate loss ratio is the true loss ratio for these accident periods, but in other cases users may want to explicitly account for measurement error or uncertainty in the ultimate loss ratio estimates. Currently, our SSM model is the only model that explicitly accounts for measurement error.

Note that despite our models being formulated to use ultimate loss ratios as the target variable, ultimate losses and earned premiums are used as input data to fit the models. All forecasting models use the ultimate losses and premiums to compute loss ratios for modeling internally, and resulting outputs (i.e. predictions) are given back on the loss scale (i.e. ultimate losses as opposed to ultimate loss ratios).

Available Models

• Autoregressive Lag 1 Model (AR1)
  • Model Fit Configuration
  • Model Predict Configuration
• State Space Model (SSM)
  • Model Fit Configuration
  • Model Predict Configuration
• Generalized Cape Cod Model (TraditionalGCC)
  • Model Fit Configuration
  • Model Predict Configuration